1977 Optimal Design of Mixed-Media Packet-Switching ... Design of...Optimal Design of Mixed-Media Packet-Switching Networks: Routing and Capacity Assignment AND FRANKLIN F Absrruct-This

158 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-25, NO. 1 , JANUARY 1977

Optimal Design of Mixed-Media Packet-Switching Networks: Routing and Capacity Assignment

AND FRANKLIN F

Absrruct-This paper considers a mixed-media packet-switched computer communication network which consists of a lowdelay terrestrial store-and-forward subnet combined with a low-cost high-bandwidth satellite subnet. We show how to route traffic via ground and/or satellite links by means of static, deterministic procedures and assign capacities to channels subject to a given linear cost such that the network average delay is minimized, Two operational schemes for this network model are investigated: one is a scheme in which the satellite channel is used as a slotted ALOHA channel; the other is a new multiaccess scheme we propose in which whenever a channel collision occurs, retransmission of the involved packets will route through ground links to their destinations. The performance of both schemes is evaluated and compared in terms of cost and average packet delay tradeoffs for some examples. The results offer guidelines for the design and optimal utilization of mixed-media networks.

I . INTRODUCTION

I N recent years two major packet-switched communication techniques are becoming increasingly important in the de-

sign of large computer communication networks: one technique is to store-and-forward packets over terrestrial communication links; the other technique is to transmit packets over a random multiaccess radio or satellite channel.

Up to the present, the studies and implementations have been centered on networks utilizing solely either terrestrial [e.g., Advanced Research Projects Agency Network (ARPANET), National Physical Laboratory Data Network [ l] , etc.] or satellite (e.g., ALOHANET) links. Recently ARPA has augmented its terrestrial network with packet satellite communication between the US. and the United Kingdom via INTELSAT IV using satellite interface message processors (SIMP’s) built by Bolt Beranek and Newman Inc. (BBN) [ 2 ] . This multiple-access broadcast system was initiated in Septem- ber 1975 and is expected to include four ground stations shortly. TELENET Communication Corporation, one of the new value-added carriers [3], announced a plan t o offer public

Manuscript received March 24, 1976; revised September 15, 1976. This work was supported in part by the ALOHA System, a research project at the University of Hawaii, which is supported by the Advanced Research Projects Agency, Department of Defense, and monitored by NASA Research Center under Contract NAS2-8590.

D. Huynh was with the ALOHA System, University of Hawaii, Honolulu, HI 96822. He is now with IBM System Communications Division, Kingston, NY 12401.

H. Kobayashi was with the University of Hawaii, Honolulu, HI 96822, as a Consultant to the ALOHA System Project, on leave from the IBM Tbomas J. Watson Research Center, Yorktown Heights, NY 10598.

F. F. Kuo was with the University of Hawaii, Honolulu, HI 96822. He is now with the Office of the Secretary of Defense, Washington, DC 20301.

KUO, FELLOW, IEEE

packet-switched data service in which initially terrestrial and eventually satellite links will be available. Therefore, it is of great interest and importance to investigate, or at least to extend the current knowledge to cover, such a mixed-media packet-switched computer communication network.

Our mixed-media network model consists of a terrestrial store-and-forward packet-switching network, referred to here as the ground subnet, and a multiaccess/broadcast satellite which, together with the associated SIMP’s, forms the satellite subnet. The store-and-forward ground subnet can be imple- mented to provide a low delay by using, for example, leased lines of low error rate. This, however, makes the network necessarily expensive. The satellite subnet, on the other hand, is subject to the intrinsic propagation delay of about 0.26 seconds, but its cost per channel bandwidth is substantially less than that of the ground links. Therefore, the combina- tion of high-delay low-cost satellite subnet that operates in contention mode and a low-delay high-cost ground subnet that operates in queueing mode into an overall system model presents many interesting problems.

It is our goal in this paper to examine a number of key issues in the design of the proposed mixed-media packet- switching network. Assuming that network topology and traffic characteristics are given, we concentrate ?n the following problems in the present paper: 1) routing of packets via ground or satellite links; 2) capacity assignments for ground and satellite channels; and 3) retransmission strategies.

Routing procedures have been investigated using various approaches [4] -[7] . The routing we will consider is a deterministic procedure, which optimizes the overall average packet delay given a set of link capacities and message traffic characteristics. This is the approach taken by Kleinrock [4], Felperin [ 5 ] , Fultz [ 6 ] , and Cantor and Gerla [7] in their studies on optimal determi:nistic routing for a terrestrial store-and- forward network; their results will be used here to obtain the optimal routing for our mixed-media network model. A capacity assignment problem in communication networks was first formulated by Kleinrock [4] , who assumed the linear cost model and a continuum of channel capacities. We solve our capacity assignment problem using the same approach and find tradeoffs between cost and overall average packet delay.

We also investigate two operational schemes for satellite channels: one is a scheme in which the satellite channel is used as a slotted ALOHA channel as discussed by Kleinrock and Lam [8], [9] ; the other is a new multiaccess scheme we propose, in whic:h no retransmissions are attempted via satellite channel; whenever a channel collision occurs, retransmis-

HUYNH e t a l . : DESIGN OF MIXED-MEDIA PACKET-SWITCHING NETWORKS 159

Sion of the involved packets will route through ground links to their destinations. These two different schemes will be compared in terms of such performance measures as overall average delay of a packet, maximum allowable traffic loads, capacity requirements, etc.

The proposed network model consists of the following. 1) A set of store-and-forward IMP-like devices intercon-

nected by capacity-limited ground channels (a connected, distributed subnet). For the sake of reliability this subnet is at least two-connected.

2 ) A set of SIMP-like devices directly connected to satellite ground stations. These SIMP’s are usually geographically scattered and relatively far apart from each other. IMP’s and SIMP’s all have buffering and scheduling capabilities.

3) A multiaccess/broadcast satellite transponder linking all SIMP’s in a star configuration. The SIMP’s together with the broadcast satellite channel will be referred to as a satellite subnet.

In this network model we assume that the network is regionalized. That is, the network is partitioned into regions, Each region contains a SIMP and a number of IMP’s. An IMP can only access its regional SIMP. In this study we assume that the number of SIMP’s and their locations are given a priori. A SIMP is usually colocated with an IMP at some node. The regionalization of IMP’s is determined by the closeness of an IMP to a SIMP in terms of the number of hops and the distances between them. Such a structure is shown in Fig. 1.

In the following, we first review previously known results which are important to our studies, and at the same time we develop those analyses which arc pertinent to our network model but have not been considered before. We then proceed on to formulate and solve the related design problems.

11. SATELLITE SUBNET MODEL

The satellite subnet consists of a set of SIMP’s which are linked together via a satellite multiaccess/broadcast chanhel. Each SIMP is equipped with buffering and scheduling capabil- ties. The satellite channel model we will use is based upon the ALOHA technique of random-access synchronous time- division multiplexing [ 101 , [ 1 11 . We assume throughout this study that the satellite channel is time-slotted [8], but as to multiaccessing methods, we consider two different schemes: one is the slotted ALOHA, and the other is a new scheme which we name multiaccess satellite with terrestrial retransmission (MASTER).

Scheme I: Slotted ALOHA

In our satellite subnet the user population consists of a set of SIMP’s, and we assume that each SIMP is provided with sufficiently large buffer capacity that new arrivals will never be blocked. Similarly a SIMP is capable of transmitting a new packet, even when previously sent packets are outstanding due to collisions.

Lam [9] has made an extensive study of slotted ALOHA proposed for a satellite communication system. His result on a finite population model without blocking is given in terms of

MULTI-~CESS/BROADCAST SATELLITE

.

Fig. 1. Proposed network model.

* . * Computed Points Usmg Equation (2.2) The number associated with each curve represents the number of SIMPS In

. . c

. * . . . . . . .

% $ 30 b

20

l o 1 0 ‘ 0 I I I I I 1

I .2 .3 .4 .5 6 throughpi /pockefs/s/ofsJ

Fig. 2. Comparisons of curves obtained by simulations in Lam [9] and by curve-fitting (2).

throughput-delay curves as shown in Fig. 2. These curves were obtained using simulation rather than by analysis and assumed equal input rates from all users and uniform retransmission and rescheduling delays. A rescheduling delay results from a scheduling conflict in which one or more packets are sched- uled to transmit in a slot. The scheduling conflict is resolved by first sending the high-priority packet and rescheduling the other packets for later slots. An important result from his simulation study is that when the satellite system has M = 10 users, its throughput-delay tradeoffs approximate those of an infinitely many user popuiation.

If there were only one SIMP transmitting, i.e.,M = 1, then there should be no contention in the channel. Thus the delay

160 IEEE TRANSACTIONS ON COMMUNICATIONS, JANUARY 1977

over the satellite subnet consists of the propagation delay and the average queueing delay; the latter component can be derived from the result of anM/D/1 queueing system:

TABLE I PARAMETERS OF (2)

# Of a/M) blM) ni

I I I

2 .531 3.059

3‘ .528 4.674

where 5 ,494 5.871

10 489 7.219

7 s average packet delay (seconds) T , ~ ~ 0.26 second: delay time due to propagation delay u = 1,2, ..e, M . Th.en the probability qu , that SIMP u attempts C, satellite channel capacity (bits/s) a packet transmission in a given time slot, is x, total input rate to (hence throughput rate from)

the satellite channel (packets/s) qu =-, hU u = 1,2;-,M ( 3 ) 1/11, packet length (bits/packet). P S C S

For M > 1 we found that a simple modification of (1) is very where C, [bitsls] is the capacity of multiaccess satellite chan- satisfactory to those curves obtained by simulation in a man- nel and 1/11, [bitslpacket] is the packet size as defined earlier. ner as indicated by Fig. 2. We define random sequences Xu(h) and Y,(h) by

( 2 ) X & ) = 1, if SIMP u transmits in slot h

0, otherwise

where a(M) represents the degradation factor of channel capacity due to collision. From (1) and the known result on an infinite population model we have a(1) = 1 and lim M+w a(M) = l/e. The other parameter b(M) gives another degree of freedom for us to fit the curves in the vertical direction. The set of parameters found are tabulated in Table I .

Scheme 11: MASTER

A possible drawback of the ALOHA scheme as applied to the satellite subnet is that each time a packet needs a retransmission, its delay time must be increased at least by the 0.26 seconds due to the inherent propagation delay of the satellite channel. Furthermore if the message traffic rate exceeds some critical level, the number of backlog packets will rise sharply, and will further increase the occurrence of collisions. This positive feedback effect will possibly result in an avalanche of collisions: the channel utilization will rise up to almost 100 percent, yet the throughput will suddenly drop to virtually zero. This “instability” problem of the slotted ALOHA is discussed by Kleinrock and Lam 191.

This observation had led us to propose a new scheme, in which all retransmissions by SIMP’s are carried out through the ground subnet, and retransmitted packets are rerouted from the originating SIMP’s to their destination IMP’S directly via ground without going through the destination SIMP’S. We will refer to this technique as MASTER. In this scheme, there will be no outstanding packets in the satellite subnet, and no packet will experience more than one roundtrip propagation delay over the satellite channel. If the ground subnet is not as congested as the satellite subnet, then we not only improve the

. overall delay response, but also ensure the stability of the system.

Since MASTER has never been analyzed previously, let us consider the throughput-delay tradeoffs here. Suppose that the satellite subnet has M SIMP’s. Let h, [packets/s] be the average message rate from SIMP u to the satellite channel,

and

1 , if SIMP u successfully transmits in slot h

0, otherwise (5) YU@) =

for u = 1,2, - - ,M, and h = 1,2,3, .-. Certainly, X,(h) = 1 if Yu(h) = 1 , but not vice versa. If X&) = 1 and Y,(h) = 0 , then the attempted transmission is a failure due to channel collision.

From the definitions of (3) and (4) it follows that

P[X,(h) = 1 3 := qo (6 )

and

P[X,(h) = 01 = 1 - qu 6 Go (7)

for u = 1,2, -,M, and all h. Furthermore, by assuming that the input message sequences

‘from different SIMP’s are statistically independent, we readily obtain the following properties for the sequences Y,(h).

I I

P[Yu(h) = 11 = 40 n 47 qupu (8) 7 f u

where Pa represents the probability of success of any attempt transmission from SIMP u.

The throughput So [packets/slot time] of the satellite channel is therefore given by

M M so = P[Y,(h)= 11 = quPu.

u=l u=l

Since the input (or offered) traffic is


the difference between SI and S o , M

o = l

is the portion of the packet flows that are rerouted via the ground subnet.

If we assume that message flows from regional IMP’s to a SIMP can be characterized by a Poisson process, and that nodal processing delays can be very small compared with channel queueing delays, then the average delay To [s/packet] experienced by a packet successfully traveling from SIMP u through the satellite channel is given by

where the last term is the average waiting time obtained from an MIDI1 queueing model.

The overall average packet delay over the satellite channel rS [s/packet] can then be obtained by averaging To’s:

where

M X, = X,[packets/s]

o = l

is the total input rate to the satellite channel. Note that the condition for the individual queue to be stable is X, < pSCs,

u = 1, 2, ..., M, rather than X, < p,C,. This is because those packets which require retransmissions are not placed on the satellite channel and rerouted to the ground.

For the purpose of this paper (1 3) is all we need. For further information concerning MASTER, the reader is referred to a companion paper by the authors [ 131 .

111. GROUND SUBNET MODEL

The ground subnet is a store-and-forward distributed network. In accordance with the two different operational schemes of the satellite subnet, we discuss the following two cases for the ground subnet model. In Scheme I (i.e., slotted ALOHA), under which the satellite subnet uses slotted ALOHA without blocking, the ground subnet, has only originally assigned ground traffic (Le., only one type of traffic). In Scheme I1 (i.e., MASTER), under which SlMP’s divert all retransmissions to the ground net, IMP’s can either add these retransmission to their originally assigned packet flows on a first-come, first-served (FCFS) basis, or give these retransmission packets a higher ,priority, by holding off, but without preempting, regular packets flow. Under the FCFS case, the operations of the ground subnet associated with

’ \

L.

Scheme I and Scheme I1 are the same. Under the priority scheduling scheme, the IMP’s should be equipped with a facility to manipulate traffic with two priority classes.

For a queueing network with general structure, a closed- form analytic solution has been obtained only under the Markovian assumption: that is, the origination of messages from sources (IMP nodes in our model) should be characterized by Poisson processes, and the service times (message lengths) are independent and identically distributed (iid) with exponential distributions. The Poisson assumption has been statistically validated in several empirical studies of data traffic (see [14] , [15]). The length of packets in our ground subnet is assumed to be variable with a possible constraint on the maximum allowable packet size. As long as the coefficient of variation (i.e., the ratio of standard deviation to mean) of the packet size distribution is not far from unity, the exponential assumption should be quite reasonable. However, the length of a packet, once generated at the originating IMP, should remain unchanged throughout the entire transmission over different links within the network; the independence assumption stated above certainly is not realistic in this regard, but it seems that this assumption is not so critical for the analysis of such performance measures as throughput and the average delay. It may well be a poor assumption if one is interested in esti- mating the delay of a particular packet or in the delay distribution rather than just the average value. As for further discussions on these assumptions the reader is referred to Kleinrock [4] , [ 161 who reports the validation of such a model based on simulation studies.

Under the Markovian assumptions made above, we can apply the well-known decomposition theorem due to Jackson [I71 and its recent extension by Baskett et al. [18] and Kobayashi and Reiser [19] . Hence the average delay T, [s/packet] , that a packet experiences due to queueing and transmission over the link I, is

in which XI [packets/s] is the total message flow over link I , CI [bits/s] is the capacity of that link, and l/p [bits/packet] is the average length of a packet.

A remark is in order concerning (15). This formula holds not only under the FCFS scheduling rule but under a large class of disciplines, which are often referred to by the name of “work-conserving’’ queueing disciplines [20] . This class includes the case with two class priority scheduling described earlier. Furthermore,.it has been shown recently [I91 that in order for (15) to apply, the message-routing behavior can be any stochastic or deterministic one, as long as it can be characterized by a Markov chain of some order. Furthermore, we can assume arbitrary number of different classes, as long as their routing behavior is concerned (we still have to assume, however, that all messages are coming from the common distribution, which is an exponential distribution of mean 1/p. This last property allows us to assume different routing pat- terns depending on the origin of messages. A deterministic split traffic (bifurcated) routing strategy to be discussed later


is certainly a particular case of general routing behavior to which the simple formula (15) applies. Note that the traffic rates {X,} over the individual links will differ depending on the routing pattern or algorithm to be chosen.

IV. ROUTING

With a mixed-media network the issue of routing is a major concern. With two possible courses to choose from-one via satellite and one via ground-the issue is to choose the set of routes so as t o minimize the overall average network delay. The tradeoffs to consider are these: the satellite channel has an inherent minimum delay of 0.26 seconds. However, satellite capacity is less costly than. ground channel capacity for medium to long distances, and therefore more satellite capacity is available .at less cost than comparable facilities on the ground. The ground channels are inherently faster than the satellite channel, but because of capacity limitations, are subject to queueing delays, which combined with the store-and- forward nodal processing delays, may, in heavy traffic situations, result in larger overall delays than the satellite delays. To ‘summarize, satellite channels have greater delays but also’more cost effective channel bandwidth than ground channels.

The routing procedure used in the ARPANET is a distributed adaptive algorithm in which each node has a routing table which is periodically updated with minimum distance estimates from its immediate neighbor [6] . In our case study to follow, we have chosen a deterministic split traffic routing strategy [6] which because it allows traffic to flow on more than one path between a given source-destination node pair, gives a better balance than a fixed routing procedure. We wish t o emphasize, however, that our analytical model does not require any specific routing algorithm, but can accommodate any that are static and can be modeled mathematically.

Suppose we are given a network of N nodes with a specified topology which includes a satellite channel of capacity C, [bitsls] , a set of ground links capacities C, [bits/s] (I = 1,2, *.; L ) , and a demand matrix [yij] ,where yij [packets/s] is the average rate of messages originated at node (IMP) i and destined for node (IMP) j , i,j = 1, 2, -., N. The routing problem is to optimally assign the traffic demand iij’s along different paths of ‘the network so that the resulting overall average packet delay is minimized. Note that the link traffic rate X, (1 = 1,2, ..., L ) defined in the preceding section is uniquely determined . . by the demand matrix [yij], the routing rule, and retransmission strategy.

Let us define the traffic splitting factor gij as the fraction of the traffic, originated at node i and destined for node j , which goes through the ground subnetwork. It is clear that gij = 1 if IMP’S i and j are in the same region. We definegij by

This fraction (Sij) of the traffic is first routed to the regional SIMP of IMP i, sent through the satellite channel to the regional SIMP of IMP j , and finally directed to the destination IMP j . Of courses this sequence of steps takes place only when

the transmission over the satellite channel is successful. If a collision takes place, two different courses of action follow, depending on the scheme assumed; in case of the ALOHA channel (i.e., Scheme I), the collided packets will attempt retransmission through the satellite channel, whereas in the MASTER channel (i.e., Scheme II), these packets will be rerouted to the ground subnet.

In both the slotted ALOHA and MASTER schemes, the overall average delay T for a packet traveling from its origin to destination 1s given’by

where

y = yij = total traffic rate in the network. I J

The definition of X l and X,, and derivations of the average delay Tl and T , were already, discussed in Sections I1 and 111. In [2 1, appendix 111 we derive the expressions for XI and Xu in terms of { g i j } and {-yij}.

Having derived the expression for the overall average packet delay, we can now state formally our routing problems as follows: given network configuration, traffic demand matrix [yij], and link capacities Cl’s and C,,

min T subject to ( 0 < g i j < 1, for all ij}. (1 8) {gijl

In the system with slotted ALOHA channel (i.e., Scheme I), the average delay T l of those packets sent from SIMP u (u = 1,2, ..., M) over the satellite subnet is equal to r, of (2), if the traffic demand and routing are such that the input rates from all the SIMP’S into the satellite channel are well balanced, I.e.,

Those packets which go through the ground link 1 will experience the average delay of Tl given by (15). Thus the overall average delay of a packet during its entire travel in the net is, from (2), ( I 5), and (1 6),

1 L X, Xsrm in

Y 1=1 Ilc; - hz Y T = - -- +-

For the scheme with MASTER channel (Scheme 11) the average delay To for packets from SIMP u is given by (12). The average delay that a packet receives in its transmission over the ground link 1 is given by Tz of (15), irrespective of the scheduling rule chosen. Therefore, by substituting these equations into (16) we obtain the following expression for the

HUYNH e t al. : DESIGN OF MIXED-MEDIA PACKET-SWITCHING NETWORKS 163

overall delay which a packet receives in the net under Scheme 11:

In (21), the traffic rate X, over the ground link I includes not only the originally assigned ground traffic, but also the traffic due to those packets which are rerouted from SIMP’s after unsuccessful transmissions over the satellite channel.

For the class of deterministic and probabilistic routing rules we discussed earlier, we can show that both T of (20) and that of (21) are convex functions of gij, i, j = 1, 2, -., N. The reason is as follows: as discussed earlier the traffic rates X, (1 = 1,2, .-, L ) , X, (u = 1,2, -, M), and As are all linear with respect to gij , and T’s of (20) and (21) are both convex functions with respect to X,, X,, and As. Because of the convexity, the set of {g i j } that minimize T can be found by any optimization procedure. In numerical computations of the case study problems we used Box’s COMPLEX optimization algorithm [22] . This method is a sequential search technique which has proven effective in solving problems with nodinear objective functions subject to nonlinear inequality constraints. It has an advantage over gradient methods in that no derivatives are required. It also tends to find the global optimum due to the fact that the initial set of starting points are randomly scattered throughout the feasible region. Moreover, its rate of convergence has been shown to be better than Rosenbrock’s algorithm [22]. In [21, appendix 1111 we show the flow chart and give a brief description of this optimization procedure.

Example 1: Consider the network with eight nodes (IMP’s) and twenty links shown in Fig. 3. In this net there are two regions consisting of nodes {1,2,3,4} and nodes {5,6,7,8}, respectively, and the regional SIMP’s are located at nodes 1 and 7. The traffic demand matrix is assumed to be uniform with yij = 20 [packets/s] for all i # j and yii = 0 for all i = 1, 2, .*., 8, and the average packet length is assumed to be 5 12 bits on all ground channels. The packet length on the satellite channel is fixed and equals 1 kbit. The ground link capacities are all assumed to be 50 kbits/s, i.e., C, = 5 X 104 [bits/s] for all 1 = 1, 2, -., 20, and the satellite capacity to be C, = 1.5 X lo6 [bits/s] .

The ground subnet routing we used in this example is the split traffic routing (or alternate routing) which is based on the minimum number of hops required to transmit packets from a given source node to a destination node. For example, if we want to send packets from IMP 1 to IMP 8 via the ground net, the minimum number of hops between IMP’s 1 and 8 is four, and there are four alternate paths of four hops: they are path a) 1 + 3 -+ 5 + 7 + 8; path b) 1 -+ 3 -+ 5 -+ 6 -+ 8; path c) 1 + 3 + 4 -+ 6 -+ 8; and path d) 1 + 2 + 4 + 6 + 8. At any node along the paths selected above, if there are two links of the selected paths emanating from the node, then the traffic rate is bifurcated equally on each of. these two links. For instance the traffic coming into IMP 3 will be split into links 8 and 0 equally. Using this ground subnet routing algorithm

SATELLITE

?

/ocoiion of m /MP

@ /mi& of m /MP ond o S/MP

Fig. 3. Network model with two SIMP’s and eight IMP’s.

TABLE I1

TO REGION 2 ROUTING INDEXES FOR TRAFFIC FROM REGION 1

for ALOHA &stMtion

1 5 6 7 8

/ I 1 0 0 0

,855 ,681 0 ,706 I 0 ,315

4 1 1 0 1 T= ,229 saccmds

1 . 5 6 7 . 8

I ,889 0 0 0

o n M 2 1 I ,995 0 ,394 3 1 I ,025 ,692 4 I I ,817 0 ,805

T= ,526 seconds 4-

we find that the traffic assignments between IMP’s 1 and 8 are 1/8 of the total traffic 71.8 over path a), 1/8 over path b), 1/4 over path c), and 1/2 over path d).

After obtaining these split factors for each node pair and adding them up appropriately, we obtain the link traffic X, for each l = 1, 2, -., 20. Because of the symmetry of both the network topology and traffic demand matrix, balanced traffic is maintained throughout the net by use of the ground subnet routing algorithm discussed above.

With the above data as input to the routing optimization program, the routing indexes gij for both ALOHA and MASTER are computed and are given in Table 11. Also shown in Table I1 are the minimum overall average delays of 0.229 seconds for the network using ALOHA and 0.326 seconds for the network using MASTER. ALOHA outperforms MASTER. This is not too surprising; here satellite capacity is much larger than the ground capacities (C, = 1.5 X lo6 bits/s > C, = 5 X 104 bits/s). In addition, the ground capacities are shared by intraregional traffic. (Recall that gij = 1 if IMP’s i and j reside in the same region.) Thus, the optimum average delay points fall inside the region favoring ALOHA. At the end of this paper, we show how this difference can be narrowed by a reassignment of the capacities subject to a fixed linear cost.


In Table 11, only routing indices for traffic from Region 1 to Region 2 are shown. Because of the symmetry of the network and demand matrix, the routing indices for traffic from Region 2 to Region 1 are symmetrical to those from Region 1 to Region 2. For instance, for network using MASTER scheme (lower table),gs2 =gzs = 0.394;g7, =gI8 = 0; etc.

V. CAPACITY ASSIGNMENTS

In the packet-routing studies of the previous section we assumed that the ground link capacities and the satellite channel capacity are given. Now we proceed to the capacity assignment problem; that is, we wish to minimize the, total average message delay T under the total budget constraint. We assume as given the topology of the network (including SIMP locations), and the demand matrix [yij]. Furthermore we assume, in the present section, that the routing indexes [gij] are given; hence the link traffic X I , 1 = 1, 2 , -e., L and the satellite channel traffic X, are also known. (The last assumption will be removed in Section VI which will discuss the joint optimization problem.)

We can formulate the capacity assignment problem as

L . '

minimize T subject to E bZC1 + b,C, < B (22) { d , c, 1 = 1

where Tis given by (20), i.e.,

M T = - & T z + x AaTa .

Y [ z=1 a = l 1 The parameter b, [ co~ t /b i t - s -~ ] of ( 2 2 ) is the cost of the satellite channel per unit traffic rate [bit/s] ; similarly bz is the cost factor of link 1, 1 = 1 , 2 , -, L.

The optimization problem defined by (22) and (23) is quite difficult if the capacities must be chosen from a discrete set of options. Following Kleinrock [4] we assume that the capacities of ground links and satellite channel are continuous variables and use analytic procedures involving Lagrange multi- pliers similar to that used by Kleinrock in his capacity assignment problem [4] . We now outline our solutions for the two different schemes.

Scheme I: Slotted ALOHA The (continuous) capacity assignment problem is to mini-

mize T of (20) subject to the following equality constraint: L

B = x bzC; + b,C,. 1 = 1

By using the .well-known Lagrange multiplier method, we could obtain closed form expressions for the optimal values of C, and C,. This would involve, however, solving fourth-order algebraic equations, which would result in rather complicated solutions.

The solution can be greatly simplified, however, if we slightly modify the result of (20) which we write

The difference between T of (20) and its approximation is

which is negligibly small compared with the second !term of (25) since

PsCsTmin 9 1 (27)

which holds practically for any value of C, in the range of our interest. Minimization of involves only second-order algebraic equations, and the optimal set of capacities are given by

and

where

bzAz fi=- YP

and

We can interpret the above result as follows. The first term XJp of (28) is the minimum required capacity of link 1. If Cz were less than this critical value the link 1 would become un- stable. Similarly, the first term of (29) is the lower bound of the satellite capacity, below which the ALOHA channel will completely collapse. The constant fi defined by (31) represents the cost of the link 1 per unit level of the total traffic 7. Similarly f, is that of the satellite channel. The value B, defined by (30) represents the critical budget below which the network cannot accommodate the given traffic level y. According to (28) and (29), the remaining budget B-B, is

HUYNH e t 42.: DESIGN OF MIXED-MEDIA PACKET-SWITCHING NETWORKS 165

distributed among all the links and satellite in proportion to where the critical budget B,* is now &, 1 = 1 , 2 , ‘ e - , L, and m 2 , respectively.

The substitution of (28) and (29) into (25) leads to blhl b,X, B,* = x- +-. (39) 1=1 P P 8

The minimized ?=possesses the same form as that of (33): min T=- ” --_--- + -

(33) Y B - B,

which is a hyperbola function of B.

Scheme II: MASTER We now minimize T of (21) with the same budgetary con-

straint, i.e., (24). Because of the reason similar to that discussed in Scheme I , we attempt to minimize, instead, the following objective function F:

The difference

is again negligibly small compared with the second term of (34); their ratio is equal to the ratio of one half of packet time 1/2psC, to the propagation time rmin = 0.26 seconds. The modified function (34) is still not suitable to optimization; the last term consists of M components (a = 1,2, ..., M) each of which has the common value of C, in the denomina- tor. Thus, in order to obtain a closed form solution for optimal solution, one has to deal with an algebraic equation of degree 2M. By further assuming that the traffic rates from SIMP’s are well balanced, we use the approximation

Although the two schemes discussed above give similar results [(33) versus (40)], their performance comparison is not so simple as it may appear. If all the traffic rates Al, I = 1 , 2 , ..+, L and X, were common for both cases, then clearly Scheme I1 should achieve a better performance than Scheme I , since B,* < B, (recall that the values a(M) obtained in Section I1 are all smaller than unity, hence smaller than M ) . The assumption made above, however, never holds. Even when the same set of routing indexes{gij} and the ground subnet routing rule are applied to both of the schemes, the ground traffic hl, 1 = 1, 2, -., L are different, though the values of X, will be the same. In Scheme I1 the link traffic XI includes not only the originally assigned portion but the traffic rerouted . from SIMP’s, which will increase B,*. Note also the values f i are different under the two different schemes, because of the difference in X1.

Since the link traffic is dependent on the routing indices gij , we cannot separate the capacity assignment problem from the routing problem.

VI. JOINT OPTIMIZATION OF ROUTING AND CAPACITY ASSIGNMENTS

In the previous two sections we treated the problems of routing and capacity assignments separately. The optimal solution of one problem, however, depends on the solution of the other; thus we need to seek joint optimization of the problems. Let us denote by g the set of routing indexes{gij; 1 < i, j < N } , and by C the set of link capacities {el, 1 < I < N, C,} . Similarly let h be the set of link and channel traffics { X l , 1 < 1 < L, X,} which, in- turn, is a function of g. We can write our objective function T as

Then the objective function T (34) reduces to that of (25) ’ T = T(x(g),c) except that a(M) is to be replaced by M. Hence the optimal sets of Cl and C, are and our joint optimization problem as

(3 7) minimize T subject to 0 <g < 1

8 , c L

and 2 blC, + b,C, GB. 1=1

and It seems quite unfeasible to attempt to minimize the above

X, B - B,* m 2 function dire.ctly with respect to g and C. We instead seek the (38) optimum solution g* and C* according to the iterative numer-

ical procedure schematically shown in Fig. 4. Brief discussions

c, =-+ - . I J f l bs 5 f i + m 2

1=1 of each block follow.


starting point is to the optimum solution; the speed of con-

?--' CHOOSE INITIAL SET k = l ESTIMATES

I I(INCREASE k BY 111 I

ALGORITHM

8

Fig. 4. Flow chart for joint optimization of routing and capacity assignment.

Blocks 1 and 2: Set the iteration step index k equal to one, and choose the initial estimates g(l) and Cc1). For the specified ground subnet routing algorithm and the operational scheme of satellite channel (i.e., ALOHA channel or MASTER channel), A( l ) . is computed from the given demand matrix [ - y i j ] for the chosen gel). With this initialization, enter the iterative cycle by increasing the index k t o k + 1 .

Blocks 3 and 4: For the parameters c ( k ) and X(k ),, the routing algorithm of Section IV yields the optimum routing indices g ( k + l ) and the corresponding performance index T R ( k + l ) -

Blocks 5 and 6: With the updated link traffic h (k+ l ) = X(g(k+l)), we then use the analytic solution method of See- tion v to find the optimum capacity assignment C(k+l), and the corresponding delay p ( k + l ) .

Blocks 7 and 8: The average packet delay F ( k + l ) is an improvement over TR(k+l)within the same cycle step (k + 1). Hence it follows always that p ( k + l ) < T R ( k + l ) . If the improvement is less than a sufficiently small parameter E > 0 (a priori set value), then we judge the minimum point has been achieved, and stop the whole procedure. Otherwise go back to Block 2 and iterate the same cycle.

From the above description, we see that each iteration is a two-stage optimization; in the first stage the set of link capacities is fixed, and T is minimized over the set of traffic splitting factors, whereas in the second stage, the set of traffic splitting factors is fixed and T is minimized by the choice of link capacities. Since T is a convex function with respect to both C and g, the optimum solution can be achieved within the error determined by E . In fact, for the numerical examples t o follow, with E = 10-5 seconds, each optimum point is obtained after 10-20 iterations depending on how close the

vergence is quite reasonable. Example 2: As ,an example of this joint optimization, let us

again consider the network model of the routing example (Example l), depicted in Fig. 3.

In solving the capacity assignment problem we need to know the total allowable budget and unit cost of ground and satellite channel capacities. We assume the unit cost of the ground channel capacities are identical, so we can normalize all costs by the unit cost of ground channel capacity. In obtaining the follomwing results, we further assume a ratio of 1 to 10 for satellite and ground channel capacity costs, i.e., 1 unit cost of ground channel capacity equals 10 unit cost of satellite channel capacity. Our program is general enough so that we can assume any ratio between satellite capacity and ground capacity costs. Perhaps a more realistic ratio to use today is a 1 to 3 proportion. The input data consist of the original demand matrix, initial values of C, = 50 kbits/s and C, = 1500 kbits/s, and an assumed total budget B in ground channel cost units and bl = 1 and b, = 0.1.

We have performed a number of runs with different values of budget B and the results are given in Fig. 5. We see that the throughput-delay tradeoff curves, after the removal of the assumption made in Section V that the link traffic rates are fixed, are again hyperbolic. As shown in Fig. 5, network under ALOHA tends to perform better than network under MASTER. Recall that we have observed this fact in the routing example. As seen in Fig. 5 for the 2-SIMP case, the difference in the delays is reduced as compared with the results in the previous routing example (27 percent relative to MASTER'S delay value there i.n comparison with 21 percent here). Never- theless, the results are still in favor of ALOHA. Notice that the delay differences between ALOHA and MASTER are negligible for budget ranging from B = 1 300 000 cost units to B = 1 700 000 cost units. As B drops below 1 300 000 cost units, the delay curve of MASTER departs from that of ALOHA. A reasonable explanation for these outcomes is as follows. When the budget B is sufficiently large, one has money to spend on the more expensive ground channel capacities; therefore, most traffic go through the lower delay ground subnet.,(Recall that the satellite subnet-delay is at least 0.26 seconds.) Since satellite channel traffic is small, the difference between ALOHA and MASTER disappears; their performances are thus similar. When budget becomes small, the ground subnet alone cannot support the entire traffic load, more and more traffic is diverted to.the satellite channel, and the distinction between MASTER and ALOHA becomes apparent. Since we have assumed a 10 to 1 cost ratio in favor of satellite channel, more capacity is assigned to the satellite subnet and less to the ground subnet. As we know, the larger the satellite channel capacity, the better ALOHA 'performs, whereas the smalkr the ground channel capacities, the poorer MASTER performs. Altogether these make ALOHA outper- form MASTER.

Example 3: To further clarify the problem let us consider an 8-region network shown in Fig. 6 with same configuration as the previous ex.ample, but each node now has an IMP and a SIMP. It is a network with 8 IMP'S and 8 SIMP'S. We assume


1.4-

1.2-

e ‘.O- s

P

2-

,0571 .Os5

, 0 3 6 8

,0368 7 .8 .9 1.0 1.1 1.2 1.3 1.4 115 16 1.7

budget m mdlton un/t costs of ground chonnel copac;ty

Fig. 5. Delay-cost tradeoffs for network with eight IMP’s and two SIMP’s.

SATELLITE 2

/ocalim of an /MP

@ /om?& of an IMP and o SIMP

Fig. 6 . Network model with eight IMP’s and eight SIMP’S,

that the demand matrix, mean packet lengths, and unit-cost ratio remain the same as before. For ALOHA, however,a(M) and ‘b (M) are now estimated to be 0.492 and 6.724, respectively. Results for this network model are depicted in Fig. 7. It is seen that this network model has generally smaller delay than the previous one. This is because of the addition of 6 more S1MP’s.l The network under ALOHA is again superior to that under MASTER, and the difference is more substantial. This is a general trend: as the number of SIMP’s is increased, more traffic goes through the satellite channel, which draws more capacity from the total, and ground subnet gets less of its share. This puts MASTER in a disadvantageous position relative to ALOHA. For the same network (shown in Fig. 6)

of IMP’S and SIMP’s to reflect this addition. Another way of looking Unfortunately, our mathematical model does not include the cost

at this problem is: the cost of the SIMP’s has been averaged out and included in the cost unit b,; so by retaining the same cost ratio, we essentially assume that the effe.ctive cost of the satellite channel in this example is even lower than that in the previous case.

:3 I

Fig. 7. Delay-cost tradeoffs for network with eight IMP’S and eight SIMP’s and ten to one cost ratio.

i 1 . 1 1.3 1.5 badget in ml11,on unrr costs of ground chnnel mpnnty

I 7

Fig. 8. Delay-cost tradeoffs for network with eight IMP’s and eight SIMP’s and three to one cost ratio.

and parameters, if we now reduce the cost ratio to 3 : 1, we obtain different results which are depicted in Fig. 8. As seen in Fig. 8, again, when the budget B > 1 500 000 cost units, no distinction exists between ALOHA and MASTER, but, when B < 1 500 000 cost units, MASTER is slightly better than ALOHA, since now the cost ratio is advantageous for ground subnet, ground channels get more of their share of the total capacity, and excessive capacity in the ground subnet favors MASTER.

CONCLUSIONS

In this paper we have presented some of the important design issues for mixed-media packet-switching networks. Satellite packet switching has considerable promise for low- cqst high-bandwidth data communications. However, there is inherent high delay in satellite links which does not appear in ground links. Therefore, a mix of the two communication mkdia seems to offer the best of both worlds. In this paper we have examined a number of tradeoffs which offer guidelines for the design and optimum utilization of mixed-media networks. We have introduced a new communication scheme called multiaccess satellite with terrestrial retransmission

168

(MASTER) with the hope that it would offer significant advantages over slotted ALOHA. Results of this paper show that MASTER does work better than ALOHA under certain circumstances, but not always so. The capacity assignment, determined by the cost ratio of ground and satellite channels, determines which system is better. Also, the greater sensitivity t o small changes in traffic of ALOHA may make MASTER the better system for many applications.

The fact that neither of the two schemes is clearly dominant suggests that a,mixture of both might be the best system. When a channel collision occurs in such a system, retransmissions can go either again through the satellite subnet, as in ALOHA, with some.probability 6 , or through the ground subnet, as in MASTER, with probability 1 - 6. The probability 6 would be chosen to minimize the average packet delay. This idea will be explored further.

In this paper we have not included the cost of IMP’S and SIMP’S in our model. We have also not explored the possibility of sending network control information along the ground and using the satellite for bulk data transmission. Another logical extension of the MASTER scheme will be to use the satellite channel on a reservation basis, such as suggested by Crowther et al. [23], Roberts [24], and Binder [ 2 5 ] , but use the ground channel to set up reservations. We plan to explore these ideas in a subsequent paper.

REFERENCES D. L. A. Barber and D. W. Davies, “The NPL data network,” in Proc. Conf. Laboratory Automation, Novosibirsk, U.S.S.R., Oct. 1970; also NPL Com. Sci. T.M. 4 7 (NIC 14671), Oct. 1970. S. Butterfield, R. Rettberg, and D. Walden, “The satellite IMP for the ARPA network,” in Proc. 7th Hawaii Int. Conf. System Sciences-Subcon. Cornput. Nets, Jan. 1974, pp. 70-73. B. D. Wessler and R. B. Hovey, “Public packet-switched networks,” Datamation, pp. 85-87, July 1974. L. Kleinrock, Communication Nets: Stochastic Message Flow and Delay. New York: Dover, 1964. K. D. Felperin, “Interactive techniques for evaluation of command-control store-and-forward net performance,” Stanford Res. Inst., Stanford, CA, Tech. Note TN-CDS-1, 1969. G. L. Fultz, “Adaptive routing techniques for message switching computer-communications networks,” Ph.D. dissertation, Dep. Comput. Sci., Univ. of California, Los Angeles, available as rep.

D. G. Cantor and M. Gerla, “Optimal routing in a packet- switched computer network,” IEEE Trans. Comput., vol. C-23,

L. Kleinrock and S. S. Lam, “Packet-switching in a slotted satellite channel,” in AFIPS Nut. Comput. Conf. Proc., vol. 42, June 1973, p. 703. S. S. Lam, “Packet-switching in a multi-access broadcast channel with application to satellite communication in a computer network,” Ph.D. dissertation, Dep. Comput. Sci., Univ. of Cali- fornia, Los Angeles, available as rep. UCLA-ENG-7429, Apr. 1974. N. Abramson, “The ALOHA System,” in Colnputer-Communica- tion Networks, N. Abramson and F. F. Kuo, Eds. Englewood Cliffs, NJ: Prentice-Hall, 1973, pp. 501-518. F. F. Kuo and N. Abramson, “Some advances in radio communications for computers,” in Dig. Papers-COMPCON ’73, San Francisco, CA, Feb. 1973, pp. 57-60. L. G. Roberts, “ALOHA packet system with and without slots and capture,” Stanford Res. Inst., Stanford, CA, ARPANET Satellite Syst. Note 8 (NIC 11290), June 1972. D. Huynh, H. Kobayashi, and F. F. Kuo, “Design issues for mixed media packet switching networks,” in Proc. Nut. Comput.

UCLA-ENG-7252, July 1972.

pp. 1062-1069, Oct. 1974.

IEEE TRANSACTIONS ON COMMUNICATIONS, JANUARY 1977

Conj , AFIPS Cwzf. Proc., vol. 45. Montvale, NJ: AFIPS Press,

[14] E. Fuchs and P. E. Jackson, “Estimates of distribution of random variables for certain computer communications traffic models,” in Proc. ACM Symp. Optimization of Data Communi- cations Systems, Oct. 1969, pp. 202-225.

1151 P. A. W. Lewis and P. C. Yue, “Statistical analysis of series of events in computer systems,” in Sthtistical Computer Perform- ance evaluation, W. Freiberger, Ed. New York: Academic,

1161 L. Kleinrock, “Performance models and measurements of the ARPA computer network,” in Proc. NATO Advanced Study Inst. Computer Communication Networks, R. L. Grimsdale and F. F. Kuo, Eds. Noordhoff International, 1975, pp. 63-88.

1171 J. R. Jackson, “Job shop-like queueing systems,” Management Science, vol. 10, p. 131, Oct. 1963.

[18] F. Baskett, K. M. Chandy, R. R. Muntz, and F. G. Palacios, “Open, closed, and mixed networks of queues with different classes of customers,” J. Ass. Comput. Mach., vol. 22, pp. 248- 260, Apr. 1975.

[ 191 H. Kobayashi and M. Reiser, “On generalization of job routing behavior in a queueing network model,” IBM Thomas J . Watson Res. Center, Yorktown Heights, NY, res. rep. RC 5679, Oct. 1975.

120) L. Kleinrock, “A conservation law for a wide class of queueing disciplines,” Naval Res. Log. Quart., vol. 12, pp. 181-192, 1965.

[21] D. Huynh, H. Kobayashi, and F. F. Kuo: “Optimal design of mixed-media packet-switching networks: Routing and capacity assignment,” IJniv. of Hawaii, Honolulu, ALOHA Syst. Tech. Rep. B76-3, Mar. 1976.

[22] M. J . Box, “A new method of constrained optimization and a comparison with other methods,” Comput. J., p. 42, Aug. 1965.

(231 W. Crowther et al., “A system for broadcast communications: Reservation A’LOHA,” in Proc. 6th Hawaii Int. Con6 System Sciences, Jan. 1.973, pp. 371-374.

[ 241 L. G. Roberts, “Dynamic allocation of satellite capacity through packet reservation,” in AFIPS Nut. Comput. Conf. Proc., vol. 42, p. 711, June 1973.

1251 R. Binder, “A dynamic packet switching system for satellite broadcast channels,” Univ. of Hawaii, Honolulu, ALOHA Syst. Tech. Rep. B74-5, Aug. 1974.

1976, pp. 541-549.

1972, pp. 265-280.

* Dieu Huynh (S’76-M’76), for a photograph and biography, see this issue, page 157.

* Hisashi Kobayashi (S’66-M’68-SM’76), for a photograph and biography, see this issue, pages 28-29.

* Franklin F. Kuo (S’56-M’58-F’72) was born in China in 1934. He received the B.S., M.S., and Ph.D. degrees in electrical engineering from the University of Illinois, Urbana, in 1955, 1956, and 1958, respectively.

He has worked at the General Electric Com- pany, Bell Telephone Laboratories, and Law- rence Radiation Laboratory. He has taught at the Polytechnic Institute of Brooklyn, the Uni- versity of Colorado, and was Professor of Elec-

Computer Sciences at the University of Hawaii from 1966 to 1975. He trical Engineering and of Information and

was also a consultant to the Electronics Engineering Department of the Lawrence Radiation Laboratory during 1966-1971. From June 1971 to September 1972,.he was on leave from the University of Hawaii and was a Liaison Scientist with the Office of Naval Research

IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-25, NO. 1, JANUARY 1977 1 69

in London, England. From September 1972 to December 1975 he was Director, then Technical Director of the ALOHA System, a computer communications research project sponsored by the Defense Advanced Research Projects Agency. The major development of the project was the ALOHANET, a packet broadcasting radio network for use over ground radio and satellites. He is now Assistant Director (Teleprocess- ing/ADP) in the Office of the Director of Telecommunications and Command and Control Systems, Office of the Secretary of Defense, Washington, D.C. In that capacity he has program management respon- sibility fcr the new digital data networks, SATIN IV and AUTODIN 11, as well as for the overall World Wide Military Command and Control

System (WWMCCS) ADP program. He is also the author, coauthor, or coeditor of 6 books and over 40 technical papers.

Dr. Kuo was a member (1966-1972) of the COSINE (Computer Sciences in Electrical Enginering) Committee of the National Academy of Engineering. He is Vice Chairman of the ACM Special Interest Group on Data Communications (SIGCOMM), a member of IFIP Working Group 6.1, International Network Working Group (INWG), and a member of the IEEE Communications Society, Computer Communi- cation Technical Committee. He is listed in Who’s Who in America, American Men and Women of Science, Outstanding Educators of America, and Who’s Who in Engineering.

The Organization of Computer Resources into a Packet Radio Network

Abstract-Packet radio communications provides an effective way to interconnect fixed and mobile computer resources. The ALOHA Sys- tem at the University of Hawaii first introduced this capability in the context of a single-hop system using off-the-shelf RF equipment with aU terminals within line of sight of the central station. The packet radio network described in this paper is I) an extension of the basic Hawaii work to a geographically distributed system involving the use of re- peaters to achieve area coverage beyond line of sight, and 2 ) provides added capabilities for authentication, antijam protection, and coexistence with other possibly different systems in the same band. An overview of the packet radio system concept is given in this paper.

I INTRODUCTION

N this paper, we describe the use of packet radio communication for organizing computer resources into a computer

communications network. A system to demonstrate the packet radio concept is being developed by the Advanced Re’search Projects Agency (ARPA). Initial testing in the San Francisco area began in 1975. The attributes of this system are presented and its application to mobile radio communications and computer architecture is briefly discussed.

The development of packet switching has made possible the economic sharing of computer resources [23], [24], [36] over a wide geographic area and, as a valuable byproduct, it has provided an effective alternative to circuit switching in providing error-free wide-band communication networks [27] , [30] . The basic architecture of a resource sharing computer network includes Host computers connected to one or more packet switches which may be co-located or remote from the Hosts. The packet switches are interconnected by point-to- point data circuits according to a topological design which results in low-cost networks for a given target throughput,

Manuscript received January 27, 1976. This paper was presented at

The author is with the Advanced Research Projects Agency, Arling- the National Computer Conference, Anaheim, CA, 1975.

ton, VA 22209.

reliability, and delay [14] , [29] . For a given packet switching technology, it is possible to increase network throughput greatly by assembling a higher performance switch out of a cluster of lower performance switches (see Fig. 1) and by providing many more circuits between clusters [22] . An alternate approach which uses multiple minicomputers to obtain a higher performance switch is described in [2 11 .

The use of packet broadcasting techniques for interconnec- tion becomes attractive when the number of minicomputers (or microprocessors!) is sufficiently large and the overall traffic flow is small. The use of wire “busses” for packet broadcasting appears certain to be an effective interconn’ection technique. However, packet radio provides another alternative that may be useful for organizing the communications among a large or even a small number of computer resources regardless of the physical setting; inside a box, within a room, or throughout a wide geographic area (see Fig. 2). In addition to its utility for mobile communications, packet radio may eventually result in the development of improved techniques for maintenance, breadboarding, and packaging of computer equipment.

For a geographically distributed network, economic studies have shown that the cost of local distribution for a large user population can be a significant part of the overall system cost [ l l ] . For this reason alone, it would be desirable to identify more economic techniques for local data distribution than the use of telephone lines. Some progress in this direction has already taken place [28] and further development of cable systems is expected. However, even if the cost of telephone access lines were not a dominant factor, an effective means of obtaining mobile access would still be required. This has provided one incentive for the development of a local radio distribution system. The burst characteristics of computer communication [31] will surely be significantly different from the characteristics of mobile radio telephone. By using packet

1977 Optimal Design of Mixed-Media Packet-Switching ... Design of...Optimal Design of Mixed-Media Packet-Switching Networks: Routing and Capacity Assignment AND FRANKLIN F Absrruct-This

Documents