Randomized policy of a poisson input queue with J vacations

Jau Chuan Ke*, Kai Bin Huang, W.l. Pearn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

This paper studies the operating characteristics of an M/G/1 queuing system with a randomized control policy and at most J vacations. After all the customers are served in the queue exhaustively, the server immediately takes at most J vacations repeatedly until at least N customers are waiting for service in the queue upon returning from a vacation. If the number of arrivals does not reach N by the end of the Jth vacation, the server remains idle in the system until the number of arrivals in the queue reaches N. If the number of customers in the queue is exactly accumulated N since the server remains idle or returns from vacation, the server is activated for services with probability p and deactivated with probability (1 - p). For such variant vacation model, other important system characteristics are derived, such as the expected number of customers, the expected length of the busy and idle period, and etc. Following the construction of the expected cost function per unit time, an efficient and fast procedure is developed for searching the joint optimum thresholds (N*, J*) that minimize the cost function. Some numerical examples are also presented.

Original languageEnglish
Pages (from-to)50-71
Number of pages22
JournalJournal of Systems Science and Systems Engineering
Volume19
Issue number1
DOIs
StatePublished - 1 Mar 2010

Keywords

  • < p, N >-policy
  • Cost
  • Supplementary variable technique
  • Vacation

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