Abstract: We present a prioritized, limited multi-server processor sharing (PS) system where each server has various capacities, and N (≥2) priority classes are allowed in each PS server. In each prioritized, limited server, different service ratio is assigned to each class request, and the number of requests to be processed is limited to less than a certain number. Routing strategies of such prioritized, limited multi-server PS systems that take into account the capacity of each server are also presented, and a performance evaluation procedure for these strategies is discussed. Practical performance measures of these strategies, such as loss probability, mean waiting time, and mean sojourn time, are evaluated via simulation. In the PS server, at the arrival (or departure) of a request, the extension (shortening) of the remaining sojourn time of each request receiving service can be calculated by using the number of requests of each class and the priority ratio. Utilising a simulation program which executes these events and calculations, the performance of the proposed prioritized, limited multi-server PS rule can be analyzed. From the evaluation results, most suitable routing strategy for the loss or waiting system is clarified.
Abstract: We propose a novel prioritized limited
processor-sharing (PS) rule and a simulation algorithm for the performance evaluation of this rule. The performance measures of practical interest are evaluated using this algorithm. Suppose that there
are two classes and that an arriving (class-1 or class-2) request encounters n1 class-1 and n2 class-2 requests (including the arriving
one) in a single-server system. According to the proposed rule, class-1
requests individually and simultaneously receive m / (m * n1+ n2) of the service-facility capacity, whereas class-2 requests receive 1 / (m *n1 + n2) of it, if m * n1 + n2 ≤ C. Otherwise (m * n1 + n2 > C), the arriving request will be queued in the corresponding class waiting
room or rejected. Here, m (1) denotes the priority ratio, and C ( ∞), the service-facility capacity. In this rule, when a request arrives at [or
departs from] the system, the extension [shortening] of the remaining
sojourn time of each request receiving service can be calculated using
the number of requests of each class and the priority ratio. Employing
a simulation program to execute these events and calculations enables
us to analyze the performance of the proposed prioritized limited PS
rule, which is realistic in a time-sharing system (TSS) with a
sufficiently small time slot. Moreover, this simulation algorithm is
expanded for the evaluation of the prioritized limited PS system with
N 3 priority classes.