The EPRCA (Enhanced Proportional Rate Control Algorithm) is a leading congestion control protocol for Available Bit Rate (ABR) service in ATM networks. This paper shows that this protocol is only marginally stable: once a queue is congested, then its queue size will eventually decrease. However, if a queue is not congested, its queue size can actually increase and a congestion can be self-induc...

We discuss how long range dependence can innuence the characteristics of a single server queue. We take the analogue of the G/M/1 queue except that the input stream is altered to exhibit long range dependence. The equilibrium queue size and equilibrium waiting time distributions each have heavy tails. By suitably selecting the parameters of the inputs, the queue size or waiting time can be made...

This paper studies load balancing for many-server (N servers) systems. Each server has a buffer of size b − 1, and can have at most one job in service 1 jobs the buffer. The time follows Coxian-2 distribution. We focus on steady-state performance policies heavy traffic regime such that normalized system is λ = N−α 0 < α 0.5. identify set achieve asymptotic zero waiting. include several classica...

We consider a Lévy-driven tandem queue with an intermediate input assuming that its buffer content process obtained by a reflection mapping has the stationary distribution. For this queue, no closed form formula is known, not only for its distribution but also for the corresponding transform. In this paper we consider only light-tailed inputs. For the Brownian input case, we derive exact tail a...

In this paper we examine a tandem network of queueing nodes where a nonstationary external Markovian arrival process feeds the initial upstream node. We develop methods for modeling the departure flow from any upstream node in its role as the arrival process to the immediate downstream node, and employ various techniques to match the interarrival moments to the downstream node to the moments of...

The EPRCA (Enhanced Proportional Rate Control Algorithm) is a leading congestion control protocol for Available Bit Rate (ABR) service in ATM networks. Even though the EPRCA has been adopted by the ATM forum as the standard for ABR congestion control, we show that this protocol is only marginally stable. The stability analysis presented in this paper does not consider interactions among network...

Several Active Queue Management (AQM) techniques for routers in the Internet have been proposed and studied during the past few years. One of the widely studied proposals, Random Early Detection (RED), involves dropping an incoming packet with some probability based on the estimated average queue length at the router. The analytical approaches to obtaining average drop probabilities in a RED en...

We consider a Lévy-driven tandem queue with an intermediate input assuming that its buffer content process obtained by a reflection mapping has the stationary distribution. For this queue, no closed form formula is known, not only for its distribution but also for the corresponding transform. In this paper we consider only light-tailed inputs, and derive exact asymptotics for the tail distribut...

Abstract This paper considers a parallel queueing model with two servers, where arriving customers join the shortest queue. In [14], we studied a similar queueing model, and obtained the tail decay rate of the stationary distribution by using the matrix analytic approach. The main objectives of this paper are to extend the result in [14] to a more general model, and to clarify difficulty when w...

We consider an M/G/1 queue with symmetric service discipline. The class of symmetric service disciplines contains, in particular, the preemptive last-come-first-served discipline and the processor-sharing discipline. It has been conjectured in Kella, Zwart and Boxma [1] that the marginal distribution of the queue length at any time is identical for all symmetric disciplines if the queue starts ...