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

A versatile model for TCP bandwidth sharing in networks with heterogeneous users.

Enabled by the emergence of various access technologies (such as ADSL and wireless LAN), the number of users with high-speed access to the Internet is growing rapidly, and their expectation with respect to the quality-of-service of the applications has been increasing accordingly. With TCP being the ubiquitous underlying end-to-end control, this motivates the interest in easy-to-evaluate, yet accurate, performance models for a TCP-based network shared by multiple classes of users. Building on the vast body of existing models, we develop a novel versatile model that explicitly captures user heterogeneity, and takes into consideration dynamics at both the packet level and the flow level. It is described how the resulting multiple time-scale model can be numerically evaluated. Validation is done by using NS2 simulations as a benchmark. In extensive numerical experiments, we study the impact of heterogeneity in the round-trip times on user-level characteristics such as throughputs and flow transmission times, thus quantifying the resulting bias. We also investigate to what extent this bias is affected by the networks' `packet-level parameters', such as buffer sizes. We conclude by extending the single-link model in a straightforward way to a general network setting. Also in this network setting the impact of heterogeneity in round-trip times is numerically assesse

Sojourn times in the M/G/1M/G/1 queue with deterministic feedback

In this paper we consider an M/G/1 queueing model, in which each customer is fed back a fixed number of times. For the case of negative exponentially distributed service times at each visit, we determine the Laplace-Stieltjes transform of the joint distribution of the sojourn times of the consecutive visits. As a by-result, we obtain the (transform of the) total sojourn time distribution; it can be related to the sojourn time distribution in the M/D/l queue with processor sharing. For the case of generally distributed service times at each visit, a set of linear equations is derived, from which the mean sojourn times per visit can be calculated

Performance modeling of a bottleneck node in an IEEE 802.11 ad-hoc network

This paper presents a performance analysis of wireless ad-hoc networks, with IEEE 802.11 as the underlying Wireless LAN technology. WLAN has, due to the fair radio resource sharing at the MAC-layer, the tendency to share the capacity equally amongst the active nodes, irrespective of their loads. An inherent drawback of this sharing policy is that a node that serves as a relay-node for multiple flows is likely to become a bottleneck. This paper proposes to model such a bottleneck by a fluid-flow model. Importantly, this is a model at the flow-level: flows arrive at the bottleneck node, and are served according to the sharing policy mentioned above. Assuming Poisson initiations of new flow transfers, we obtain insightful, robust, and explicit expressions for characteristics related to the overall flow transfer time, the buffer occupancy, and the packet delay at the bottleneck node. The analysis is enabled by a translation of the buffer dynamics at the bottleneck node in terms of an M/G/1 queueing model. We conclude the paper by an assessment of the impact of alternative sharing policies (which can be obtained by the IEEE 802.11E version), in order to improve the performance of the bottleneck