Study of multi server retrial queueing system under vacation policies by direct truncation method

  • Authors:

  • Muthu Ganapathi Subramanian;Ayyappan Govindan;Gopal Sekar

  • Affiliations:

  • Tagore arts College, Pondicherry, India;Pondicherry Engineering College, Pondicherry, India;Tagore arts College, Pondicherry, India

  • Venue:
  • Proceedings of the 6th International Conference on Queueing Theory and Network Applications
  • Year:
  • 2011

Quantified Score

Hi-index 0.00

Visualization

Abstract

Consider a Multi server Retrial queueing system with vacation policies in which arrival rate follows a Poisson distribution with parameter λ and service time follows an exponential distribution with parameter μ. Let c be the number of servers in the system. Two type of vacation policies have been introduced in this paper namely exhaustive service type vacation and Bernoulli vacation. If any one of the server is free at the time of a primary call arrival, the arriving call begins to be served immediately by one of the idle servers and customer leaves the system after service completion. Otherwise, if c servers are busy or c servers are in vacation then the arriving customer goes to orbit and becomes a source of repeated calls. The pool of sources of repeated calls may be viewed as a sort of queue. Every such source produces a Poisson process of repeated calls with intensity σ. If an incoming repeated call finds any one of the servers is free, it is served and leaves the system after service, while the source which produced this repeated call disappears. The access from the orbit to the service facility follows the classical retrial policy. This model is solved by using Direct Truncation Method. Numerical study have been done for Analysis of Mean number of customers in the orbit, Mean number of busy servers, Mean number of servers in vacation, Truncation level and various system measures.