Population effects in multiclass processor sharing queues
نویسندگان
چکیده
Consider a single server queueing system with several classes of customers, each having its own renewal input process and its own general service times distribution. Upon completing service, customers may leave, or reenter the queue, possibly as customers of a different class. The server is operating under the egalitarian or the discriminatory processor sharing discipline. In this paper, we consider the fluid approximation of this multiclass processor sharing queue. We first provide the results allowing to compute the trajectories for this model, under the egalitarian PS discipline. Asymptotic results for overloaded queues are also stated. Next, we show that a simple transformation allows to compute the solution for the discriminatory PS queue as well. Finally, we illustrate the different results through numerical experiments. We compare transient trajectories with simulations, and we discuss the fairness issue that may arise in overloaded PS queues.
منابع مشابه
On the equivalence between multiclass PS-type scheduling policies
Consider a single server queue serving a multiclass population. Some popular scheduling policies for such a system (and of interest in this paper) are the discriminatory processor sharing (DPS), discriminatory random order service (DROS), generalized processor sharing (GPS) and weighted fair queueing (WFQ). The aim of this paper is to show a certain equivalence between these scheduling policies...
متن کاملMultivariate Rational Approximants for Multiclass Closed Queuing Networks
ÐClosed Markovian networks of queues with multiclass customers and having a product form equilibrium state probability distribution are useful in the performance evaluation and design of computer and telecommunication systems. Therefore, the efficient computation of the normalizing function, the key element of the solution in product form, has attracted considerable effort. We consider a networ...
متن کاملLaw of Large Number Limits of Limited Processor-Sharing Queues
Motivated by applications in computer and communication systems, we consider a processor sharing queue where the number of jobs served is not larger than K. We propose a measure-valued fluid model for this limited processor sharing queue and show that there exists a unique associated fluid model solution. In addition, we show that this fluid model arises as the limit of a sequence of appropriat...
متن کاملAsymptotic behavior of generalized processor sharing queues under subexponential assumptions
We analyze the behavior of Generalized Processor Sharing (GPS) queues with heavy-tailed service times. We compute the exact tail asymptotics of the stationary workload of an individual class and give new conditions for reduced-load equivalence and induced burstiness to hold. We also show that both phenomena can occur simultaneously. Our proofs rely on the single big event theorem and new fluid ...
متن کاملTail Asymptotics for Processor Sharing Queues
The basic queueing system considered in this paper is the M/G/1 processor sharing (PS) queue with or without impatience and with finite or infinite capacity. Under some mild assumptions, a criterion for the validity of the RSR (Reduced Service Rate) approximation is established when service times are heavy tailed. This result is applied to various models based on M/G/1 processor sharing queues.
متن کامل