Sojourn time asymptotics in the M/G/1 processor sharing queue

We show for the M/G/1 processor sharing queue that the service time distribution is regularly varying of index $-nu$, $nu$ non-integer, iff the sojourn time distribution is regularly varying of index $-nu$. This result is derived from a new expression for the Laplace-Stieltjes transform of the sojourn time distribution. That expression also leads to other new properties for the sojourn time distribution. We show how the moments of the sojourn time can be calculated recursively and prove that the k-th moment of the sojourn time is finite iff the k-th moment of the service time is finite. In addition, we give a short proof of a heavy traffic theorem for the sojour

The M/G/1M/G/1 queue with processor sharing and its relation to a feedback queue

The central model of this paper is anM/M/1 queue with a general probabilistic feedback mechanism. When a customer completes his ith service, he departs from the system with probability 1–p(i) and he cycles back with probabilityp(i). The mean service time of each customer is the same for each cycle. We determine the joint distribution of the successive sojourn times of a tagged customer at his loops through the system. Subsequently we let the mean service time at each loop shrink to zero and the feedback probabilities approach one in such a way that the mean total required service time remains constant. The behaviour of the feedback queue then approaches that of anM/G/1 processor sharing queue, different choices of the feedback probabilities leading to different service time distributions in the processor sharing model. This is exploited to analyse the sojourn time distribution in theM/G/1 queue with processor sharing. Some variants are also considered, viz., anM/M/1 feedback queue with additional customers who are always present, and anM/G/1 processor sharing queue with feedback

Sabisu kiritsu o koryoshita GI/GI/1 machi gyoretsu shisutemu no kakusan kinjiho ni kansuru kenkyu

制度:新 ; 報告番号:甲3539号 ; 学位の種類:博士(工学) ; 授与年月日:2012/2/25 ; 早大学位記番号:新587

Heavy-traffic limits for Discriminatory Processor Sharing models with joint batch arrivals

We study the performance of Discriminatory Processor Sharing (DPS) systems, with exponential service times and in which batches of customers of different types may arrive simultaneously according to a Poisson process. We show that the stationary joint queue-length distribution exhibits state-space collapse in heavy traffic: as the load ρ tends to 1, the scaled joint queue-length vector (1−ρ)Q converges in distribution to the product of a determin

Optimal job splitting in parallel processor sharing queues

The main barrier to the sustained growth of wireless communications is the Shannon limit that applies to the channel capacity. A promising means to realize high-capacity enhancements is the use of multi-path communication solutions to improve reliability and network performance in areas that are covered by a multitude of overlapping wireless access networks. Despite the enormous potential for capacity enhancements offered by multi-path communication techniques, little is known about how to effectively exploit this. Motivated by this, we study a model where jobs are split and downloaded over N multiple parallel networks, each of which is modeled as a processor sharing (PS) queue. Each job is fragmented, according to a fixed splitting rule α=