Two finite capacity connected queues with service in random order

This paper tries to extend Perel and Yechiali [Queues where customers of one queue acts as servers of the other queue, Queuing Syst (2008) 60:271-288]. In this paper there are two queues with general arrival time distribution Gi (γi), i= 1,2 where γI is arrival rate of ith queen, finite capacity Ni . The queue discipline is service in random order (SIRO). It is supposed the first queue has always r1 operateves. Service of failure machines of the first queue is the negative exponential distribution with mean ∝1-1 We consider two cases, here. (a)The customers of the first queues, N1, are considered as operatives of the second queue and make a set of operatives in order to repair failure machines of the second queue with negative exponential distribution mean ∝2-1. (b) Customers of the first queue repair failure machines of the second queue with the negative exponential distribution with mean (n1∝2)-1 – and with r2 operatives. Finally, for more explanations a numerical example is provided. Obtained results can be a good approximation for Perel and Yechiali's one.

Keywords:

General arrival time distribution , Service in random order , Negative