The prolonged service time at non-dedicated servers in a pooling system

In this paper, we investigate the effect of the prolonged service time at the non-dedicated servers in a pooling system on the system performance. We consider the two-server loss model with exponential interarrival and service times. We show that if the ratio of the mean service time at the dedicated server and the mean prolonged service time at the non-dedicated server exceeds a certain threshold, pooling would become unfavourable. In particular, the threshold is explicitly provided. Moreover, when the degree of the prolonged service time is pre-specified, we show that the pooling system with prolonged service time at non-dedicated servers is not preferred when the work load in the system is greater than a certain threshold.