Abstract
In this paper, we study a single server queueing system with Coxian-2 service. In Particular, we study M/C-2/M/1 queue with Coxian-2 service and exponential vacation. We assume that units (customers) arrive at the system one by one in a Poisson process and the server provides one-by-one service based on first in first out (FIFO) rule. We obtained the steady state queue size distributions in terms of the probability generating functions, the average number of customers and their average waiting time in the system as well as in the queue.
Highlights
We study a single server queueing system with Coxian-2 service
We assume that units arrive at the system one by one in a Poisson process and the server provides one-by-one service based on first in first out (FIFO) rule
In queueing theory we study situations where units of some kind arrive at a service facility for receiving service, some of the units having to wait for service, and go out after service
Summary
In queueing theory we study situations where units of some kind arrive at a service facility for receiving service, some of the units having to wait for service, and go out after service. 2) At time t, there are n − 1 units in the queue excluding one unit in phase-1 service and there is one arrival and no service completion during This case has the joint probability Ρ1n−1 (t )(λ∆t )(1− μ1∆t ). 3) At time t, there are n + 1 units in the queue excluding one unit in phase-1 service and there is no arrival, one service completion during (t,t + ∆t] and the customer decides not to take phase-2 of service, the server doesn’t take vacation with probability (1-p) 4) At time t, there are n + 1 units in the queue excluding one unit in phase-2 service and there is no arrival, one service completion during (t,t + ∆t] , and the server does not take vacation with probability (1-p) This case has the joint probability Ρ2n+1 (t )(1− λ∆t )(μ2∆t )(1− p).
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