19 - Checkout Queues: Long or Short

Summary

In daily life, we meet many examples of first-in-first-out or fifo queues that are usually simple queueing systems. A more complex multiqueueing system might on one hand involve a fan-in structure in which several separate queues have to merge at a later facility, on the other hand, involve a fan-out structure where a single queue branches to form distinct subqueues. The people, objects, customers that flow through the system, known as entities, can have attributes, such as requiring leaded or unleaded petrol, paying by cash or cheque, that they carry with them through the system.

Aims of the project

The purpose of modelling queues is two-fold. Firstly, as customers, we tend to prefer short queues in order to save time. Secondly, as business managers, we hope the service utility (i.e. the ratio of actual time when a service is utilised over the maximum available service time) is approaching 100% to maximise profits but still want to avoid long queues for the sake of customer loyalties. Therefore it is of practical interests to predict the peak times of long queues before deciding how to improve the service.

Mathematical ideas used

Statistical distributions and probabilities used here have been discussed in Chapter 6. Sparse vectors of 0s and Is, for data extraction, are generated by various conditions. Flexible vector operations will be needed.

MATLAB techniques used

The supplied M-file queue.m is mainly used, assisted by three other M-files exprand.m, normrand.m, unirand.m. There will be an extensive use of MATLAB commands plot, bar, sort, rand.