Chapter 5Queues with Delay

5.1 Introduction

The service interruptions are an unavoidable phenomenon in many real-life situations. In most of the studies of queuing systems, it is assumed that the server is available on a permanent basis as long as at least a task is present in the waiting line, but service station never fails. However, these assumptions are practically unrealistic. In practice, we often meet a case where the server may fail and can be repaired. Applications of such models may be found in the areas of computer communication network and flexible manufacturing system.

The word “delay” in queuing theory has been used with different meanings on different occasions, including the waiting time. In this book, “waiting time” is actually waiting time. The term “delay” in this book is used to mean the additional time to the service time and waiting in line that a task may have to spend in the system before completion of its service. Feedback time is not a delay time, and we refer to it as the feedback time. However, there are terms that use “delay,” but they are actually waiting time. For instance, in a normal situation, arrivals enter a system at a buffer and wait for service. If the server is busy, then an arrival has to wait for service. This is what we mean by standard “waiting time.” Another example is in computer network, wherein queuing delay is the time the packet is in a waiting line before transmission starts. The time depends on the number of packets ahead ...

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