Operations Research--Methods and Problems

By Maurice Sasieni; Arthur Yaspan | Go to book overview

CHAPTER SIX
Waiting lines

Decision situations frequently arise in which units arriving for service must wait before they can be serviced. If the laws governing arrivals, servicing times, and the order in which arriving units are taken into service are known, then the nature of this waiting situation can be studied and analyzed mathematically. In this chapter we present some of the more elementary theory of waiting lines and some simple applications.

Arriving units may form one line and be serviced through only one station, as in a doctor's office; they may form one line and be serviced through several stations, as in a barber shop; or they may form several lines and be served through as many stations, as at the checkout counters of a supermarket. In this chapter we assume only one kind of queue discipline: first-in, first-out; with a unit going into service at the moment a station becomes empty.

A general assumption running through the chapter is that the waiting-line process will eventually become "stable," in the sense that the probability that n units are waiting at any instant remains the same as time passes. We shall not treat the transient case (a waiting line whose corresponding probabilities have not yet settled down to their stable values) or the explosive case (a waiting line that increases indefinitely with time).

The various properties of a waiting line, such as the number in line at any instant or the waiting time experienced by a particular arrival,

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Operations Research--Methods and Problems

• Title Page ii
• Preface v
• Acknowledgments vii
• Contents ix
• Chapter One - Introduction 1
• Chapter Two - Probability 5
• References 39
• Chapter Three - Sampling 40
• References 69
• Chapter Four - Inventory 70
• Chapter Five - Replacement 102
• References 124
• Chapter Six - Waiting Lines 125
• References 154
• Chapter Seven - Competitive Strategies 155
• References 182
• Chapter Eight - Allocation 183
• References 249
• Chapter Nine - Sequencing 250
• References 269
• Chapter Ten - Dynamic Programming 270
• References 293
• Appendix One - Finite Differences 294
• Appendix Two - Differentiation of Integrals 304
• Index 312
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