Section: New Results

Queueing Theory

Participants : Sara Alouf, Konstantin Avrachenkov, Alain Jean-Marie, Dimitra Politaki.

Multiclass processor sharing and random order scheduling policies

In [2], K. Avrachenkov and T. Bodas (LAAS-CNRS) consider a single server system serving a multiclass population. Some popular scheduling policies for such system are the discriminatory processor sharing (DPS), discriminatory random order service (DROS), generalized processor sharing (GPS) and weighted fair queueing (WFQ). In this work, the authors propose two classes of policies, namely MPS (Multi-class Processor Sharing) and MROS (Multi-class Random Order Service), that generalize the four policies mentioned above. For the special case when the multi-class population arrive according to Poisson processes and have independent and exponential service requirement with parameter µ, they show that the tail of the sojourn time distribution for a class i customer in a system with the MPS policy is a constant multiple of the tail of the waiting time distribution of a class i customer in a system with the MROS policy. This result implies that for a class i customer, the tail of the sojourn time distribution in a system with the DPS (GPS) scheduling policy is a constant multiple of the tail of the waiting time distribution in a system with the DROS (respectively WFQ) policy.

The marmoteCore-Q tool

Using the marmoteCore platform, a tool called marmoteCore-Q has been developed by D. Politaki under the supervision of S. Alouf and A. Jean-Marie for the simulation of a family of queueing models based on the general BMAP/PH/c queue with impatience and resubmissions. There exist many special cases of this queue for which analytical results are known. Examples are: the M/M/1 queue and its finite capacity version, the M/M/c/K queue, the M/PH/1 and M/PH/$\infty$ queues, the M${}^X$/M/1 and M${}^X$/M/$\infty$ queues. Such examples are used to validate the implementation of the marmoteCore-Q tool.