Assistant, Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University; Moscow Center of Fundamental and Applied Mathematics
A single server nonpreemptive priority queueing system with renewal type input stream and multiple vacations is studied. The distributions of intervals between arrivals, service time for each priority class and vacation periods are arbitrary and absolutely continuous. The extra component method, the Laplace transform and the special integral transform are used to obtain the non-stationary joint distribution of queue length for all priority classes.
Keywords:
nonpreemprive priority queue, single server, working vacations, queue length
A one-line queueing system with two priority classes, relative priority, Poissonian input flow with random intensity and infinite number of places in queue for waiting is studied. The current intensity value is taken at the beginning of the time reckoned for the arrival of the next requirement. Successive values of the flow intensity form a Markov chain of a special kind. The heavy traffic limiting distribution of the queue length for the least
priority class is obtained.
Keywords:
Poissonian flow, random intensity, relative priority, queue length, heavy traffic
A one-line queueing system with three incoming Poissonian flows is studied. Service time distributions are general and absolutely continuous for each flow. The first class requirements have nonpreemptive priority over
the second class requirements and preemptive-repeat-different priority over the third class requirements. The second class requirements have nonpreemptive priority over the third class requirements. The heavy traffic limiting distribution of the queue length for the third class is obtained while the system load tends to 1 and time tends to infinity.
