We consider the problem of optimal routing in a multi-stage network of queues with constraints on queue lengths. We develop three algorithms for probabilistic routing for this problem using only the total end-to-end delays. These algorithms use the smoothed functional (SF) approach to optimize the routing probabilities. In our model all the queues are assumed to have constraints on the average ...

This paper presents a method for calculating steady state probabilities of M |Er|c|K queueing systems. The infinitesimal generator matrix is used to define all possible states in the system and their transition probabilities. While this matrix can be written down immediately for many other M |PH |c|K queueing systems with phase-type service times (e.g. Coxian, Hypoexponential, . . . ), it requi...

In this paper, we study the tail behavior of the stationary queue length of an M/G/1 retrial queue. We show that the subexponential tail of the stationary queue length of an M/G/1 retrial queue is determined by that of the corresponding M/G/1 queue, and hence the stationary queue length in an M/G/1 retrial queue is subexponential if the stationary queue length in the corresponding M/G/1 queue i...

Active queue management schemes like RED (Random Early Detection) have been suggested when multiple TCP sessions are multiplexed through a bottleneck buffer. The idea is to detect congestion before the buffer overflows and packets are lost. When the queue length reaches a certain threshold RED schemes drop/mark incoming packets with a probability that increases as the queue size increases. The ...

In this paper, we investigate how to design AQM with a low-pass filter (average queuing) in supporting TCP based on the well-known AIMD dynamic model sharing a common bottleneck router. Since we formulate the AQM design problem for the given TCP as a state-space model, we get two interesting and important results: 1) We derive PD-type (Proportional-Derivative) AQM structure in terms of queue le...

Recently, several gateway-based congestion control mechanisms have been proposed to support the end-to-end congestion control mechanism of TCP (Transmission Control Protocol). In this paper, we focus on RED (Random Early Detection), which is a promising gateway-based congestion control mechanism. RED randomly drops an arriving packet with a probability proportional to its average queue length (...

The RED active queue management algorithm allows network operators to simultaneously achieve high throughput and low average delay. However, the resulting average queue length is quite sensitive to the level of congestion and to the RED parameter settings, and is therefore not predictable in advance. Delay being a major component of the quality of service delivered to their customers, network o...

Recently, several gateway-based congestion control mechanisms have been proposed to support the endto-end congestion control mechanism of TCP (Transmission Control Protocol). In this paper, we focus on RED (Random Early Detection), which is a promising gateway-based congestion control mechanism. RED randomly drops an arriving packet with a probability proportional to its average queue length (i...