Abstract
This paper analyses a two-server queueing model with consultation between the servers. Each of the servers provides consultation to the other server with a preemptive priority over customers. After consultation, the services in progress will be resumed. The arrivals to the system follows a Poisson process and requirement of consultations follow mutually independent Poisson processes; the duration of consultations follow mutually independent and identical exponential distributions. The service times of the customers at the servers are assumed to follow mutually independent phase type distributions. An explicit expression for the system stability is obtained. System performance indices are computed and numerical illustrations are provided. Further we consider two particular cases of the model described. Finally, we compare these through numerical investigations.
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