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: Performance of a limited Round-Robin (RR) rule is
studied in order to clarify the characteristics of a realistic sharing
model of a processor. Under the limited RR rule, the processor
allocates to each request a fixed amount of time, called a quantum, in a
fixed order. The sum of the requests being allocated these quanta is
kept below a fixed value. Arriving requests that cannot be allocated
quanta because of such a restriction are queued or rejected. Practical
performance measures, such as the relationship between the mean
sojourn time, the mean number of requests, or the loss probability and
the quantum size are evaluated via simulation. In the evaluation, the
requested service time of an arriving request is converted into a
quantum number. One of these quanta is included in an RR cycle,
which means a series of quanta allocated to each request in a fixed
order. The service time of the arriving request can be evaluated using
the number of RR cycles required to complete the service, the number
of requests receiving service, and the quantum size. Then an increase
or decrease in the number of quanta that are necessary before service is
completed is reevaluated at the arrival or departure of other requests.
Tracking these events and calculations enables us to analyze the
performance of our limited RR rule. In particular, we obtain the most
suitable quantum size, which minimizes the mean sojourn time, for the
case in which the switching time for each quantum is considered.
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.