Minimizing expected discounted cost in a queueing loss model with discriminating arrivals

We consider a queuing loss system with heterogeneous skill based servers and Poisson arrivals. We first assume that each arrival has a vector (X-1,..., X-n) of independent binary random variables with X-i = 1 if server i is eligible to serve that arrival. The service time at server i is exponential with rate mu(i). Arrivals finding no servers that are both idle and eligible to serve them are lost. Assuming the system incurs a cost of one unit for each lost customer, our goal is to find the optimal policy for assigning arrivals to idle and eligible servers so as to minimize the expected discounted cost of the system. Later, we generalize our model by considering k server pools where each pool i is eligible to serve arrivals with probability p(i) and all servers within this pool provide service at an exponential rate mu(i). (C) 2019 Elsevier B.V. All rights reserved.