**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
- Infinite Capacity Queues (with priorities as an option)
- Approximation to Infinite Capacity Queues (with coefficients of variation as an input)
- Simulation: Finite Capacity Queues

**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.

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.

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