On queueing with customer impatience until the beginning of service

We study queueing systems where customers have strict deadlines until the beginning of their service. An analytic method is given for the analysis of a class of such queues, namely, M(n)/M/m/FCFS+G and M(n)/M/m/FCFS/K+G models. These are queues with state-dependent Poisson arrival process, exponential service times, multiple servers, FCFS service discipline, infinite or finite capacity, and general customer impatience. The state of the system is viewed to be the number of customers in the system. This will allow a unified framework for the analysis of infinite-capacity models as well as finite-capacity models. The principal measure of performance is the probability measure induced by the offered waiting time. Other measures of interest are the probability of missing deadline and the probability of blocking. Closed-form solutions are derived for some important modeling variables and parameters. The efficacy of our method is illustrated through a numerical example.