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MaxWeight scheduling algorithms provide an effective mechanism for achieving queue stability and guaranteeing maximum throughput in a wide variety of scenarios. The maximumstability guarantees however rely on the fundamental premise that the system consists of a fixed set of sessions with stationary ergodic traffic processes. In the present paper we examine(More)
For families of random walks {S (a) k } with ES (a) k = −ka < 0 we consider their maxima M (a) = supk≥0 S (a) k . We investigate the asymptotic behaviour of M (a) as a → 0 for asymptotically stable random walks. This problem appeared first in the 1960’s in the analysis of a single-server queue when the traffic load tends to 1 and since then is referred to(More)
The goal of jointly providing efficiency and fairness in wireless networks can be seen as the problem of maximizing a given utility function. In contrast with wired networks, the capacity of wireless networks is typically time-varying and not known explicitly. Hence, as the capacity region is impossible to know or measure exactly, existing scheduling(More)
Wireless multi-hop local area networks use in general scheduling schemes that assume the network capacity to be known. Indeed in most of the throughput-optimal algorithms the sources are assumed to send at a rate within the capacity region. However, measurements made on real deployments show that the network capacity is usually difficult to characterize and(More)
CSMA/CA is a popular random-access algorithm for wireless networks, but its stability properties are poorly understood. We consider a linear multi-hop network of three nodes where the neighbouring nodes interfere with each other and medium access is governed by the CSMA/CA algorithm. We assume that the source node is saturated and packets are forwarded(More)
Carrier-Sense Multiple-Access (CSMA) protocols form a popular class of random-access schemes for regulating node activity in wireless networks. We compare the continuous and the time-slotted versions of this protocol in the saturated regime, and show that continuous CSMA has higher aggregate throughput than the slotted protocol, but this comes at the cost(More)
We look at bandwidth-sharing networks where bandwidth allocations are not known to maximize a priori any utility function. Instead, we only require the allocation functions to be 0-homogeneous and concave, which are desirable properties in many situations. We show that a certain gradient condition is necessary and sufficient for such allocations to solve(More)
We consider an M/G/1 queue with subexponential service times. We give a simple derivation of the global and local asymptotics for the busy period. This analysis relies on the explicit formula for the joint distribution for the number of customers and the length of the busy period of the M/G/1 queue. 2000 Mathematics Subject Classification: 60K25, 60G50,(More)
We consider a stochastic queueing system modelling the behaviour of a wireless network with nodes employing a discrete-time version of the standard decentralised medium access algorithm. The system is unsaturated – each node receives an exogenous flow of packets at the rate λ packets per time slot. Each packet takes one slot to transmit, but neighboring(More)
The goal of jointly providing fairness and efficiency in wireless networks can be seen as the problem of maximizing a given utility function. The main difficulty when solving this problem is that the capacity region of wireless networks is typically unknown and time-varying, which prevents the usage of traditional optimization tools. As a result, scheduling(More)