SimpleQ Assignment - A Very Simple Queuing Simulation

This problem is to evaluate a banking system which is organized such that all arriving customers join a single queue if all the tellers are busy. Then, when a teller becomes free, the customer at the head of the queue goes to that teller for service.

There are three parameters to characterize our system:

• • λ : the average arrival rate of customers

  • µ : the average service rate of tellers

  • k : the number of tellers on duty in the bank

The performance measurements we desire are:

• • L_q : the average queue length

  • W_q : the average waiting time

  • W : the average time in system

If we assume that everything is perfectly random in our system, then we assume that arrivals are distributed according to the Poisson distribution and service times are distributed exponentially. The desired results may be obtained analytically, using the following formulas derived from queuing theory (you may also wish to look at the Intro to Queuing lecture notes):

HERE is a good tutorial with a quick and easy calculator so you can check your work.

Your assignment is to build several simple simulation models for this bank system, using the values below for the system parameters. Make sure your program realizes that solutions are valid only if the ratio λ / k µ is less than 1.

Use the following data:

• • λ = 25 arrivals / hour

  • µ = 30 customers / hour

  • k = 1 server (System I) and k = 2 servers (System II)

Model both Systems I and II using (a) spreadsheet (b) CLOUDES (c) Any other simulation software tool, e.g., Arena, GPSS, SIMSCRIPT, C++, Java, MATLAB, R, etc. Report values of L, Lq, W, Wq and compare to the analytic (true) values for these performance measures.

Sidebar: For part (a) you will need a formula to generate exponential random variate. The lecture on Monte Carlo Methods includes an algorithm for this, the Invers-Transform Method.