OPERATIONS RESEARCH AND MANAGEMENT SCIENCE HANDBOOK Editor: A. Ravi Ravindran September 29, 2006 Chapter 9 Queueing Theory N. Gautam Dept. of Industrial & Systems Engineering Texas A&M University, College Station
[email protected] 9.1 Introduction What is common between a fast food restaurant, an amusement park, a bank, an airport security check point, and a post office? Answer: you are certainly bound to wait in a line before getting served at all these places. Such types of queues or waiting lines are found everywhere: computer-communication networks, production systems, transportation services, etc. In order to efficiently utilize manufacturing and service enterprises, it is critical to effectively manage queues. To do that, in this chapter we present a set of analytical techniques collectively called queueing theory. The main objective of queueing theory is to 1 2 CHAPTER 9. QUEUEING THEORY develop formulae, expressions or algorithms for performance metrics such as: average number of entities in a queue, mean time spent in the system, resource availability, probability of rejection, etc. The results from queueing theory can directly be used to solve design and capacity planning problems such as: determining the number of servers, an optimum queueing discipline, schedule for service, number of queues, system architecture, etc. Besides making such strategic design decisions, queueing theory can also be used for tactical as well as operational decisions and controls. The objective of this chapter is to introduce fundamental concepts in queues, clarify assumptions used to derive results, motivate models using examples, and point to software available for analysis. The presentation in this chapter is classified into four categories depending on types of customers (one or many) and number of stations (one or many).