SOJOURN TIMES IN SINGLE-SERVER QUEUES WITH NEGATIVE CUSTOMERS

We derive expressions for the Laplace transform of the sojourn time de nsity in a single-server queue with exponential service times and inde pendent Poisson arrival streams of both ordinary, positive customers a nd negative customers which eliminate a positive customer if present. We compare first-come first-served and last-come first-served queueing disciplines for the positive customers, combined with elimination of the last customer in the queue or the customer in service by a negativ e customer. We also derive the corresponding result for processor-shar ing discipline with random elimination. The results show differences n ot only in the Laplace transforms but also in the means of the distrib utions, in contrast to the case where there are no negative customers. The various combinations of queueing discipline and elimination strat egy are ranked with respect to these mean values.