We study the parametric perturbation of Markov chains with denumerable state spaces. consider both regular and singular perturbations. By latter we mean that transition probabilities a chain, several ergodic classes, are perturbed such (rare) transitions among different classes unperturbed chain allowed. Singularly have been studied in literature under more restrictive assumptions as strong recurrence ergodicity or Doeblin conditions. relax these conditions so our results can be applied to...

While the (Egalitarian) Processor-Sharing (PS) discipline offers crucial insights in performance of fair resource allocation mechanisms, it is inherently limited analyzing and designing differentiated scheduling algorithms such as Weighted Fair Queueing Round-Robin. The Discriminatory (DPS) Generalized (GPS) disciplines have emerged natural generalizations for modeling service differentiation mechanisms. A further extension ordinary PS policy Multilevel (MLPS) discipline, which has captured...

As a natural multi-class generalization of the well-known (egalitarian) processor sharing (PS) service discipline, discriminatory (DPS) is great interest in many application areas, including telecommunications. Under DPS, mean response time conditional on requirement only known closed form when all classes have exponential distributions. For generally distributed requirements, Fayolle et al. (1980) showed that expected times satisfy system integro-differential equations. In this paper, we...

Despite measures to reduce congestion, occurrences of both recurrent and non-recurrent congestion cause large delays in road networks with important economic implications. Educated use Intelligent Transportation Systems (ITS) can significantly travel times. We focus on a dynamic stochastic shortest path problem: our objective is minimize the expected time vehicle, assuming vehicle may adapt chosen route while driving. introduce new process that incorporates ITS information model...

We analyze a generalization of the discriminatory processor-sharing (DPS) queue in heavy-traffic setting. Customers present system are served simultaneously at rates controlled by vector weights. assume that customers have phase-type distributed service requirements and allow different weights various phases their service. In our main result we establish state-space collapse for queue-length heavy traffic. The shows limit, is product an exponentially random variable deterministic vector....

We study sojourn times of customers in a processor sharing queue with service rate that varies over time, depending on the number and state random environment. An explicit expression is derived for Laplace–Stieltjes transform time conditional upon arrival amount work brought into system. Particular attention paid to mean customer as function his required work, we establish existence an asymptote tends infinity. The method change then extended include possibility varying rate. By means this...

Abstract When routing dynamically randomly arriving messages, the controller of a high-speed communication network very often gets information on congestion state down stream nodes only after considerable delay, making that irrelevant at decision epochs. We consider situation where jobs arrive according to Poisson process and must be routed one two (parallel) queues with exponential service time distributions (possibly different means), without knowing in queues. However, (conditional)...

In this paper, we focus on an admission control strategy for streaming and elastic users that enforces a minimum rate guarantee each user through pre-emptive capacity reservation. We propose approximations to estimate the performance of strategy. apply time-scale decomposition limiting regimes, non-limiting regimes novel weighted approximation. Simulation results suggest is almost insensitive traffic parameter distributions, well estimated by our proposed approximations. Our work motivated...

In this paper we obtain the scaling law for mean broadcast time of a file in P2P network with an initial population N nodes. model, at Poisson rate lambda node initiates contact another chosen uniformly random. This is said to be successful if contacted possesses file, which case initiator downloads and can later upload it other altruistic nodes (i.e., do not leave network) show that O(log(N)). free-riding nodes, our main result shows O(log(N)) achieved remain connected duration least one...

We study the joint queue length distribution of Discriminatory Processor Sharing model, assuming all classes have phase-type service requirement distributions. show that moments can be obtained by solving linear equations. use this to system in two asymptotic regimes. In first regime, different user operate on strictly separated time scales. Then we heavy traffic.

We show that different flavors of TCP may be viewed as implementations age-based scheduling disciplines. By parameterizing the disciplines interest we are able to position variants in a wide spectrum having FCFS (first-come first-served) and LAS (least attained service first) extremal policies, including PS (processor sharing) an intermediate case. argue for highly loaded systems, providing fair bandwidth allocation among all users is secondary ensuring network stability. So isolate protocol...