A Heterogeneous Bulk Service Queueing Model With Vacation

R. Sree Parimala^1,

¹Department of Mathematics, Sri Eshwar College of Engineering, Coimbatore, Tamilnadu, India

Cite this paper:
R. Sree Parimala. A Heterogeneous Bulk Service Queueing Model With Vacation. Journal of Mathematical Sciences and Applications. 2020; 8(1):1-5. doi: 10.12691/jmsa-8-1-1

Abstract

This paper is concerned with the study of bulk service M/M(a,b)/(2,1) queueing system of two heterogeneous servers with different service rates. In this model it is assumed that the arrival pattern is Poisson style with parameter λ and the service times are assumed to be mutually independent and exponentially distributed with parameters μ1and μ2 for the fast and slow servers respectively. The arrivals are served in batches according to FCFS discipline. In this model, the fast server (server 1) is always retained in the system and a delayed and single vacation policy for slow server (server 2)is discussed. The steady state solutions and the system characteristics are derived and analyzed for this model. The analytical results are numerically exemplified for different values of the parameters and levels also.

Keywords:
heterogeneous servers bulk queue delayed vacation

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