On dynamic assignment of impatient customers to parallel queues

Consider a number of parallel queues, each having unlimited capacity and multiple identical exponential servers. The service discipline in each queue is first-come-first-served (FCFS). Customers arrive according to a state-dependent Poisson process with an arrival rate which is a function of the total number of customers in the system. Upon arrival, a customer joins a queue according to a state-dependent stationary policy, where the state of the system is taken to be the number of customers in each queue. No jockeying among queues is allowed. Each arriving customer has a generally distributed deadline until the beginning.,of its service, after which it must depart the system immediately. An analytical method for the analysis of this system is given. This method is based on a Markovian view of the system in the long run. The principal measure of performance is the probability that a customer misses its deadline in the long run.