Waiting line model(or presentation)

Waiting Line ModelHamizah Binti Hamdan

Mohd Adzmien Bin Abdul Nuri

What is waiting line model

•Waiting line models consist of mathematical formulas and relationships that can be used to determine the operating characteristics (performance measures) for a waiting line

Characteristics of Performance Measure1. The probability that no units are in the system

2. The average number of units in the waiting line

3. The average number of units in the system

4. The average time a unit spends in the waiting line

5. The average time a unit spends in the system

6. The probability that an arriving unit has to wait for service

GSC-Waiting Line Model

Singe-Channel Waiting Model

Data Calculation

• Arrival Rate,λ=0.75

• Service Rate,µ=1(Based on previous case study)

• Assumptions

1. Arrival rate follow Poisson Distribution

2. Service rate follow Exponential Distribution

GSC Single Channel Calculation

2-Channel Waiting Model

Data Calculation

• Arrival Rate,λ=0.75

• Service Rate,µ=1(Based on previous case study)

• No of Channel,k=2

• Assumptions :

1. Arrival rate follow Poisson Distribution

2. Service rate follow Exponential Distribution

3. The service rate, µ is same for each channel

4. The arrivals wait in single waiting line and then move to the first open channel for service

GSC 2-Channel Calculation

Compare Single & 2 Channel

1. The average time a customer spends in the system (waiting time plus

service time) is reduced from W = 4 minutes to W = 1.1636 minutes.

2. The average number of customers in the waiting line is reduced from

Lq=2.25 customers to Lq = 0.1227 customer.

3. The average time a customer spends in the waiting line is reduced

from Wq =3 minutes to Wq = 0.1636 minute.

4. The probability that a customer has to wait for service is reduced from

Pw =0.75 to Pw = 0.2045.

Conclusion

•Suggest analyst to focus on improving service rate

•New Technology

• Increase service channel