numerical simulations for queueing systems

CE150: Transportation Planning and Design Page 1 of 1 Fall 2017

CE 150: Transportation Planning and Design October 25, 2017

Lab Objectives (by the end of this lab, you should be able to)

 Perform numerical simulations for queueing systems o Deterministic Patterns o Stochastic Patterns

 Calculate basic queue performance measures

 Estimate probabilities for stochastic queueing systems

Lab Assignment #7 due Wednesday, November 1: Simulate the arrivals and departures of 200 persons in the following two queueing systems. Assume that the total rate of arrivals to the system is 60 persons per hour and the average time of service for each server is 1 minute per customer.

a) One M/M/2 system (i.e. a single queue that is served by two servers, e.g. the Post Office)

b) Two M/M/1 systems (i.e. two separate queues, each served by an independent server, e.g. cashiers in Walmart).

 Then, compare the performance of the two systems in terms of, i) Queue lengths ii) Average wait time in the queue iii) Average time spent in the system

 Which system is better?

 How do the simulated M/M/1 measures compare to the equation ones? Why?

 You can work in pairs, given that each person completes the simulation for one of the two cases.

 Alternatively, you can receive one course bonus point if you decide to complete the simulations for both cases alone.

Outline of Likely Topics

1. Negative exponential distribution 2. Macro-enabled worksheets 3. Stochastic interarrival or service times 4. Deterministic interarrival or service times 5. System simulation 6. System performance parameters

a. Average time in queue b. Average time in system c. Queue Length

7. Probabilities of queueing measures

Case (a)

Case (b)