On queueing with customer impatience until the end of service

We study queueing systems where customers have strict deadlines until the end of their service. An analytic method is given for the analysis of a class of such queues, namely, M(n)/M/1+G models with ordered service. These are single-server queues with state-dependent Poisson arrival process, exponential service times, FCFS service discipline, and general customer impatience. We derive a closed-form solution for the conditional probability density function of the offered sojourn time, given the number of customers in the system. This is a novel result that has not been known before. Using this result, we show how the probability measure induced by the offered sojourn time is computed and consequently how performance measures such as the probability of missing deadline and the probability of blocking are obtained. This is further illustrated through a numerical example.