A fluid system with coupled input and output, and its application to bottlenecks in ad hoc networks.

This paper studies a fluid queue with coupled input and output. Flows arrive according to a Poisson process, and when n flows are present, each of them transmits traffic into the queue at a rate c/(n + 1), where the remaining c/(n + 1) is used to serve the queue. We assume exponentially distributed flow sizes, so that the queue under consideration can be regarded as a system with Markov fluid input. The rationale behind studying this queue lies in ad hoc networks: bottleneck links have roughly this type of sharing policy. We consider four performance metrics: (i) the stationary workload of the queue, (ii) the queueing delay, i.e., the delay of

Performance analysis of differentiated resource-sharing in a wireless ad-hoc network

In this paper we model and analyze a relay node in a wireless ad-hoc network; the capacity available at this node is used to both transmit traffic from the source nodes (towards the relay node), and to serve traffic at the relay node (so that it can be forwarded to successor nodes). Clearly, when a specific node is used more heavily than others, it is prone to becoming a performance bottleneck. In this paper we consider the situation that the relay node obtains a share of the capacity that is m times as large as the share that each source node receives. The main performance metrics considered are the workload at the relay node and the average overall flow transfer time, i.e., the average time required to transmit a flow from a source node via the relay node to the destination. Our aim is to find expressions for these performance metrics for a general resource-sharing ratio m, as well as a general flow-size distribution. The analysis consists of the following steps. First, for the special case of exponential flow sizes we analyze the source-node dynamics, as well as the workload at the relay node by a fluid-flow queueing model. Then we observe from extensive numerical experimentation over a broad set of parameter values that the distribution of the number of active source nodes is actually insensitive to the flow-size distribution. Using this remarkable (empirical) result as an approximation assumption, we obtain explicit expressions for both the mean workload at the relay node and the overall flow transfer time, both for general flow-size distributions

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

A fluid system with coupled input and output, and its application to bottlenecks in ad hoc networks

This paper studies a fluid queue with coupled input and output. Flows arrive according to a Poisson process, and when n flows are present, each of them transmits traffic into the queue at a rate c/(n + 1), where the remaining c/(n + 1) is used to serve the queue. We assume exponentially distributed flow sizes, so that the queue under consideration can be regarded as a system with Markov fluid input. The rationale behind studying this queue lies in ad hoc networks: bottleneck links have roughly this type of sharing policy. We consider four performance metrics: (i) the stationary workload of the queue, (ii) the queueing delay, i.e., the delay of

M/M/infinity transience: tail asymptotics of congestion periods

The c-congestion period, defined as a time interval in which the number of customers is larger than c all the time, is a key quantity in the design of communication networks. Particularly in the setting of M/M/infinity systems, the analysis of the duration of the congestion period, D_c, has attracted substantial attention; related quantities have been studied as well, such as the total area A_c above c, and the number of arrived customers N_c during a congestion period. Laplace transforms of these three random variables being known, as well as explicit formulae for their moments, this paper addresses the corresponding tail asymptotics. Our work addresses the following topics. In the so-called many-flows scaling, we show that the tail asymptotics are essentially exponential in the scaling parameter. The proof techniques stem from large deviations theory; we also identify the most likely way in which the event under consideration occurs. In the same scaling, we approximate the model by its Gaussian counterpart. Specializing to our specific model, we show that the (fairly abstract) sample-path large-deviations theorem for Gaussian processes, viz. the generalized version of Schilder’s theorem, can be written in a considerably more explicit way. Relying on this result, we derive the tail asymptotics for the Gaussian counterpart. Then we use change-of- measure arguments to find upper bounds, uniform in the model parameters, on the probabilities of interest. These change-of-measures are applied to devise of a number of importance-sampling schemes, for fast simulation of rare-event probabilities. They turn out to yield a substantial speed-up in simulation effort, compared to naïve, direct simulations

Analysis of congestion periods of an M/M/inf-queue

A c-congestion period of an M/M/infty-queue is a period during which the number of customers in the system is continuously above level c. Interesting quantities related to a c-congestion period are, besides its duration Dc, the total area AC above c, and the number of arrived customers Nc. In the literature Laplace transforms for these quantities have been derived, as well as explicit formulae for their means. Explicit expressions for higher moments and covariances (between DC,NC and Ac), however, have not beeri found so far.This paper presents recursive relations through which all moments and covariances can be obtained. Up to a starting condition, we explicitly solve these equations; for instance, we write E.DJ? explicitly in terms of ED2/0. We then find formulae for these starting conditions (which directly relate to the busy period in the M/M/infty queue). Finally, a C-intercongestion period is defined as the period during which the number of customers is continuously below level C. Also for this situation a recursive scheme allows us to explicitly com-pute higher moments and covariances. Additionally we present the Laplace transform of a so-called intercongestion triple of the three performance quantities. It is also shown that expressions for the quantities of a c-intercongestion period can be used in an approximation for the c-congestion period. This is especially useful as the expressions for the c-intercongestion period are numerically more stable than those for the c-congestion perio