OMG 402 - Operations Management Spring 1997 CLASS 6: Process Design and Performance Measurement Harry Groenevelt
Dec 31, 2015
OMG 402 - Operations ManagementSpring 1997
CLASS 6:
Process Design and Performance Measurement
Harry Groenevelt
March 1997 2
Agenda
• Recap– Basic Queuing Relationships
– Modeling a Distributed Queue
• The Impact of Variability• ‘Limited Space’ Systems and
Performance Measure Trade-offs• Capacity Strategy and Queuing Management• Summary of Insights
March 1997 3
Servers (s)
systemqueue
departuresarrivals ( customers/hr)
customers/hr/server
Recap: Basic Queuing Relationships
avg. # in system = (avg. # in queue) + (avg. # in service)
avg. # in service = (# of servers) * (utilization)
avg. time in system = (avg. time in queue) + (avg. service time)
… and remember Little’s Law!
March 1997 4
Recap: Basic Queueing Relationships
M/M/1 Queue:– Special service time and inter-arrival time
distributions (a ‘memoryless’ process)– Single Server– Average time in system = 1/(–)– Average number in system = /(-) = /(1–)
5
Recap: Basic Queuing Relationships
M/M/s Queue:– Again, memoryless arrival and service times– ‘s’ servers– Results via QMacros
G/G/s Queue:– When arrivals or service times are not of this
‘special’ type– Results via QMacros
March 1997 6
Recap: Modeling a Distributed Queue
The On-Call Computer Consultant• Customer arrives by telephone.• Information for Queue:
appointment book of the consultant• Physical Queue: Customers’ Offices• What is the ‘server’?
March 1997 7
Recap: Modeling a Distributed Queue
The On-Call Computer Consultant
When does service begin and end?• Customer point of view:
• Consultant (server) point of view:
• For QMacros, service time =
March 1997 8
Recap: Impact of variability (G/G/s)
Using QMACROS– For arrival process specify:
• Arrival Rate
• Coefficient of Variation of inter-arrival time distribution (cv(A))
– For service time distribution specify:• Service Rate
• Coefficient of Variation of service time distribution (cv(S))
March 1997 9
Recap: Impact of variability
• Reminder: if X is a random variable with mean and std. dev , then its Coefficient of Variation
= cv(X) = / • For exponential random variables:
– Coefficient of Variation = 1
• For deterministic random variables:– Coefficient of Variation = 0
March 1997 10
Recap: approximate G/G/1 formula
• An approximation for average wait in queue that works well for ‘congested’ systems:
Wq(G/G/1) = 0.5 * (cv(A)2+cv(S)2) * Wq(M/M/1)
• Use QMacros to analyze G/G/s
March 1997 11
check-in booths
queue in lobby of convention hall
departures
arrivals step off of tour buses from the hotel
Typical tasks at check-in:• ask for name and check for registration• look up registration number• check off list• hand over packetEven with seemingly plenty of booths we observe long queues. Why?
Impact of Variability: An ExampleCheck-in for an Operations Management Convention in Morocco
Original Physical Arrangement:
March 1997 12
arrivals step off of tour buses from the hotel
Impact of Variability: An ExampleCheck-in for an Operations Management Convention in Morocco
Revised Arrangement:
A-G
H-P
Q-Z
check-in booths
departures
arrivals check pre-registration information on posted computer printouts
What are the advantages of this system?
What are the disadvantages?
March 1997 13What systems can be modeled this way?
Limited Space SystemsM/M/s/N (‘limited space’) system
– Same as M/M/s system, except:
– Assumes only N positions available– An arriving customer who finds all N positions
occupied leaves without waiting and without receiving service
N in System?
Queue
Server 1
Server s
CustomerArrival
Departures
Departures
Leave Without Service
March 1997 14
Limited Space Systems: Performance Measures
Fraction Not Served: fraction of arrivals not served because they found all N positions in the system occupied
Throughput: the rate at which customers are served by the system
Load Factor: arrival rate/total capacity(how is this different from utilization?)
March 1997 15
Limited Space Systems: Performance Measures
Throughput = Arrival Rate * (1– Fraction Not Served)
• All other performance measures (time in system, etc.) are for served customers only, and satisfy all the relationships we’ve seen.
• Similar measures for M/M/s/I system with impatient customers.
March 1997 16(see: Frontiers of Electronic Commerce by Profs. Kalakota and Whinston)
Limited Space SystemsExample: Local Internet Service Provider (ISP)
N trunk lines
(all customers ‘arrive’ by same-number dialup)
national ISP andInternet Backbone
calls may queuefor a modem here
SwitchTerminal
serverRouter
Modem Farm
modem 1
modem 2
modem 3
modem s
March 1997 17
Limited Space System: Local ISP
• Each caller uses one trunk line and one modem• Arriving caller waits on a trunk line if all S
modems are used• Arriving caller busied out if N trunk lines used
lines logged onto s modemsN–s lines(virtual queue)
N trunk lines
March 1997 18
Performance measure trade-offs
Consider the system with high utilization (i.e., AOL at peak hours!)
As we decrease the number of trunk lines:• What happens to fraction not served (busied out)?
• What happens to average wait in queue?
March 1997 19(28 modems, 35 trunk lines, average session length: 20 minutes)
Performance measures trade-offNow hold the number of trunk lines constant and
increase arrival rate:
0
1
2
3
4
5
0 1 2 3 4 5 6 7 8 9 10 11 12
Arrival Rate (1/min)
Ave
rag
e W
ait
to L
og
On
(m
inu
tes)
0%
20%
40%
60%
80%
100%
Pe
rce
nt
Re
ceiv
ing
Bu
sy S
ign
als
Fraction Busy Signals(see scale on the right)
Avg Wait to Log On(see scale on the left)
March 1997 20
Performance measures trade-off
• As demand increases but capacity does not keep pace:– wait in queue increases but is limited by available
space;– percentage busied-out (not served) increases up to
100%.
– When load factors are high, customers must go somewhere!
March 1997 21
Subscriptions to AOL, 1994-1997
012345678
Jun-94 Dec-94 Jun-95 Dec-95 Jun-96 Dec-96
Nu
mb
er o
f S
ub
scri
ber
s (m
illio
ns)
January, 1997
December, 1996(flat-rate accessintroduced)
source: Jupiter Communications and the Los Angeles Times
Capacity Strategy: America Online
March 1997 22
Capacity Strategy: Expansionist
012345678
Jun-94 Dec-94 Jun-95 Dec-95 Jun-96 Dec-96
Nu
mb
er o
f S
ub
scri
ber
s (m
illio
ns)
Modem Capacity
Nr of Subscribers
March 1997 23
012345678
Jun-94 Dec-94 Jun-95 Dec-95 Jun-96 Dec-96
Nu
mb
er o
f S
ub
scri
ber
s (m
illio
ns)
Capacity Strategy: Wait-and-See
Modem Capacity
Nr of Subscribers
March 1997 25
Queuing Management
The firm’s view: • Manage demand as well as capacity
• Balance cost of service with cost of waiting (“economic optimization” at LL Bean)
• Use customer waiting time– co-production
– sales
March 1997 26
Queuing Management
The psychology of queuing:There’s more to a line than its wait (Larson)– perceived waiting time & the environment– justice– information and expectations
March 1997 27
Management of Queues:Summary of Insights
• High utilization causes congestion, high WIP and long lead times
• Variability causes congestion, high WIP and long lead times
• Multiple performance measures are often necessary to gauge true performance. Cost must be balanced with service, and the entire customer experience must be managed