New Approach for Finding Basic Performance Measures of Single Server Queue

Author:

Koh Siew Khew1,Pooi Ah Hin2,Tan Yi Fei3

Affiliation:

1. Faculty of Engineering and Sciences, Universiti Tunku Abdul Rahman, Jalan Genting Kelang, 53300 Setapak, Wilayah Persekutuan, Malaysia

2. Sunway University Business School, Sunway University, 47500 Subang Jaya, Selangor, Malaysia

3. Faculty of Engineering, Multimedia University, 63100 Cyberjaya, Selangor, Malaysia

Abstract

Consider the single server queue in which the system capacity is infinite and the customers are served on a first come, first served basis. Suppose the probability density functionf(t)and the cumulative distribution functionF(t)of the interarrival time are such that the ratef(t)/1-F(t)tends to a constant ast, and the rate computed from the distribution of the service time tends to another constant. When the queue is in a stationary state, we derive a set of equations for the probabilities of the queue length and the states of the arrival and service processes. Solving the equations, we obtain approximate results for the stationary probabilities which can be used to obtain the stationary queue length distribution and waiting time distribution of a customer who arrives when the queue is in the stationary state.

Publisher

Hindawi Limited

Subject

Statistics and Probability

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