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An Analysis of M/G/1 Vacation Systems with Restriction to the Waiting Time of the First Customer  

Hur, Sun (Department of Industrial Engineering, Hanyang University)
Lee, Jeong Kyoo (Department of Industrial Engineering, Hanyang University)
Ahn, Suneung (Department of Industrial Engineering, Hanyang University)
Publication Information
Journal of Korean Institute of Industrial Engineers / v.28, no.2, 2002 , pp. 187-192 More about this Journal
Abstract
In this paper we consider an M/G/1 queueing system with vacation. The length of vacation period may be controlled by the waiting time of the first customer. The server goes on vacation as soon as the system is empty, and resumes service either when the waiting time of the leading customer reaches a predetermined value, or when the vacation period is expired, whichever comes first. We consider two types of vacation, say, multiple vacation type and N-policy type. We derive the steady-state distributions of the number of customers at arbitrary time and arbitrary customer's waiting time by means of decomposition property. Also, the mean lengths of busy period, idle period and a cycle time are given.
Keywords
M/G/l; vacation; NT-policy; timer and counter;
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