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Markov Processes for Stochastic Modeling, 2nd Edition by Oliver Ibe

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7

Markovian Queueing Systems

7.1 Introduction

A queue is a waiting line. Queues arise in many of our daily activities. For example, we join a queue to buy stamps at the post office, to cash checks or deposit money at the bank, to pay for groceries at the grocery store, to purchase tickets for movies or games, or to get a table at the restaurant. This chapter discusses a class of queueing systems called Markovian queueing systems. They are characterized by the fact that either the service times are exponentially distributed or customers arrive at the system according to a Poisson process, or both. The emphasis in this chapter is on the steady-state analysis.

7.2 Description of a Queueing System

In a queueing system, customers from a specified population ...

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