Single Station Queueing Systems A single station queueing system, as shown in Fig. , consists of a queueing buffer of finite or infinite size and one or more identical servers. Such an elementary queueing system is also referred to as a service station or, simply, as a node. | Queueing Networks and Markov Chains Gunter Botch Stefan Greiner Hermann de Meer Kishor S. Trivedi Copyright 1998 John Wiley Sons Inc. Print ISBN 0-471-19366-6 Online ISBN 0-471-20058-1 Single Station Queueing Systems A single station queueing system as shown in Fig. consists of a queueing buffer of finite or infinite size and one or more identical servers. Such an elementary queueing system is also referred to as a service station or simply as a node. A server can only serve one customer at a time and hence it is Fig. Service station with m servers a multiple server station . either in a busy or an idle state. If all servers are busy upon the arrival of a customer the newly arriving customer is buffered assuming that buffer space is available and waits for its turn. When the customer currently in service departs one of the waiting customers is selected for service according to a queueing or scheduling discipline. An elementary queueing system is further described by an arrival process which can be characterized by its sequence of interarrival time random variables Ai A2 --- . It is common to assume that the sequence of interarrival times is independent and identically distributed leading to an arrival process that is known as a renewal process Triv82 Recent work on correlated interarrival times can be found in Luca91 and Luca93 . The distribution function of interarrival times can be continuous or discrete. We deal only with the former case in this book. 209 210 SINGLE STATION QUEUEING SYSTEMS For information related to discrete interarrival time distributions the reader may consult recent work on discrete queueing networks Dadu96 . The average interarrival time is denoted by E A Ta and its reciprocal by the average arrival rate A A d . 1 A The most common interarrival time distribution is the exponential in which case the arrival process is Poisson. The sequence B B2 of service times of successive jobs also needs to be specified. We assume that this .
