Special Topics in Queueing Theory

Special Topics in Queueing Theory

Copyright: © 2018 |Pages: 43
DOI: 10.4018/978-1-5225-5264-2.ch007
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Abstract

Topics covered in Chapter 7 are priority systems with preemptive or non-preemptive system, systems with N classes of customers, customers in groups: bulk arrivals, batch service, balking and reneging, and finite population. In a priority system, it is assumed that there are 1, 2, 3, …, N different classes or types of customers, where Type 1 customers are the most important while class N ones are the least important. When a server is available to serve a customer from the queue, the one with the highest priority level will go to the server to start their service process. In batch service, before starting the service process, a group or batch needs to be formed with a certain number of customers.
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Priority Systems

In the earlier chapters we studied systems assuming that the service priority is first in – first out, which, for want of a better expression, we could call “natural”; however we can often find systems where another service discipline is used, either because of the customers’ requirements, the urgency of service, their level of importance or because the company has to achieve a particular objective.

Let’s take the example of a hospital’s A&E department. The customers arrive at the area in a random fashion and, once they are inside, ask to be attended. Let us assume that at any given time someone with the symptoms of a cold arrives, immediately followed by someone whose life is at risk owing to a severe accident and who needs urgent attention.

If the FIFO discipline is respected, then the person with the cold would have to be served first and after they have been diagnosed and medicated then it would be the turn of the person involved in the accident. The point is that the life of the second patient depends on the speed with which he is given medical attention, whereas in the case of the first person, their symptoms are an indicator that they can wait without their life being put in danger. In this case, service priority is given to the person whose state of health is deteriorating at a faster rate. In a hospital, the care of the patient with a cold would be interrupted and service priority given to the person involved in an accident.

This example serves to illustrate a care system, known as “service priority” that is commonly used in hospital systems and, in general, in systems where the FIFO discipline is not suitable for use as a patient-care discipline.

In a priority system, it is assumed that there are 1, 2, 3, …, N different classes or types of customers, where type 1 customers are the most important while class N ones are the least important. When a server is available to serve a customer from the queue, the one with the highest priority level will go to the server to start their service process.

It is worth mentioning that when there are several customers of the same class, then the discipline that is applied to the subset of a particular class is FIFO. For the development of the respective model, we need to establish that the actions of the server, in the face of a new arrival, will be governed by one of the following considerations (Figures 1 and 2):

  • 1.

    Preemptive: Once the customer enters the server, the service process starts. However if, during the process, a customer with higher priority or importance arrives then the care process is interrupted and the customer with the lowest priority is sent to the queue and the customer with higher priority enters.

  • 2.

    Non-Preemptive: Once the customer has entered the server, the service process starts and is completed without interruptions.

Figure 1.

Preemptive. Customer of class 2 arrives and is attended but the service is interrupted when a client of class 1 arrives to the system.

Figure 2.

Non-preemptive. Customer of class 2 arrives and the service continues until the end. Customer of class 1 must wait until the end of service.

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