A STUDY ON MARKOV EVOLUTION ASSOCIATED
WITH A M/M/1/∞ QUEUING SYSTEM
S. Udayabaskaran1, M. Reni Sagaya Raj2, P. Manoharan3, A. George Maria Selvam4
1,2,3,4Department of Mathematics
Sacred Heart College
Tirupattur, 635 601, INDIA
Abstract. In this paper, we proceed to analyze a random evolution associated with the M/M/1/∞ model. The study of M/M/1/∞ queuing system has been made very extensively in the queuing literature. The system arises in a huge variety of problems of communication engineering. The object of this paper is to understand the random evolution of cost function associated with M/M/1/∞ model. This is achieved by identifying the unit cost as the fixed velocities of a random motion of a particle in a straight line.
AMS Subject classification: 60K25, 60K37
Keywords and phrases: Markov evolution, queue, idle and busy period


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DOI: 10.12732/ijam.v26i1.9

Volume: 26
Issue: 1
Year: 2013