Queue.XLS A Teaching Spreadsheet for Queuing Theory
by John O. McClain
This workbook gives a basic introduction to steady-state results for both finite and infinite capacity queues.
Instructions are included, together with a short problem illustrating each model.
There are three analytical models, and one simulation (added in May, 2003).
Finite Capacity Queues is a multi-server system with a limit to the length of the waiting line. This model assumes Poisson arrivals, exponential service time, identical servers in parallel, and newly arriving customers who balk when the queue is full. The example below is a two-server system with capacity for 5 customers waiting for service. In this example the arrival rate exceeds the service capacity, resulting in a large amount of balking. A graph of the probability distribution is available (see below), illustrating the queue's tendency to be full in such a case.
Infinite Capacity Queues is a multi-server system with no limit on the number of waiting customers. The model assumes Poisson arrivals, exponential service time, identical servers in parallel, and customers who wait as long as necessary to get service. The customers may have priorities, but the service rate is not allowed to depend on the priority class. Service is non-preemptive: the highest priority customer gets the next available server.
Approximation to Infinite Capacity Queues uses a simple formula to approximate the multi-server system with unlimited queue capacity. It also allows you to specify the amount of uncertainty in both arrivals and service time. The resulting queues are smaller as variation is reduced, reaching zero if both arrivals and service are deterministic. In the standard queuing models on the other two worksheets, the coefficients of variation are 1.0 for both service time and inter-arrival time. When CV is less than 1 the queue is smaller.
Simulation: Finite Capacity Queues uses a Visual Basic Macro to simulate the queuing system. However, it uses the Gamma distribution for service times and inter-arrival times. When the coefficient of variation is 1.0, Gamma is the Exponential, and the results converge to the Finite Capacity Queue model. Variation may be increased or decreased from 1.0. Outputs include a graph of the frequency distribution of the number in the system, plus a graph showing the convergence of the average number in the system and the probability of balking.
These simple models are intended for teaching purposes. You are welcome to use them in any manner, and change them as you see fit. This workbook comes without any guarantee whatsoever, and is distributed free of charge.
Click Here to download a copy of the Microsoft Excel Spreadsheet.