This paper highlights a few results of the Poisson queue with two heterogeneous servers studied by Krishnamoorthi (1963) under queue discipline-II that minimizes the violation of the classical ‘First Come First Served (FCFS)’ queue discipline. One special feature of this study is to solve an optimization problem relative to the service rate μ2 of the slow server is illustrated in a specific numerical exerciseto equalize the average queue length cost with that of the service cost. Further itproposes a new Poisson queue operated bytwo heterogeneous service channels with an mpolicy to yield the same steady state probability distribution of queue length and other performance measures. The two service channels provide parallel service in the former Poisson queue with an m-policy to take care of the FCFS discipline while in the proposed Poisson queue those two service channels are serially connectedsuch that each customer is served jointly by both servers according to an equivalent m-policy which perfectly implements the FCFS rule. A numerical illustration is also provided to support the fact of ‘no violation of the FCFS rule’ through a comparative method over appropriate measures.
M/(M1, M2)/2 queue, M/(M1+M2)/2 queue, Mean queue length and Mean waiting time, queue length cost and service cost
