Batch Arrival General Bulk Service Non Markovian Queueing System
Authors :
Ayyappan.G a, * and Thamizhselvi.Pb
Author Address :
a,bDepartment of Mathematics, Pondicherry Engineering Colege, Puducherry-605 014. India.
*Corresponding author.
Abstract :
This paper deals with a batch arrival and a general bulk service queueing system with single server, for which customers arrive in the system follows compound Poisson stream and the service follows general bulk service rule. The maximum number of customers to be served in one batch is b (capacity), but the server does not starts service until a (quorum, less than b) customers have accumulated; and the service time follows a general distribution. Probability generating functions of the distributions $P_n$ and $P_ n^+$ , under equilibrium, have been derived by using supplementary variable technique. An expression has been derived for the expected value of the queue size and its relation with the expected value of the waiting time of a customers has been
explored.
Keywords :
Batch Arrival, Bulk Service and Average Queue size
DOI :
Article Info :
Received : August 10, 2015; Accepted : September 29, 2015.
