Showing papers by "Arzad A. Kherani published in 2006"

Route lifetime based optimal hop selection in VANETs on highway: an analytical viewpoint

Abstract: We consider the problem of optimal next-hop selection in a route between two vehicles, for a simple scenario of Vehicular ad hoc networks (VANETs) on a highway. For a given approximation of the optimal number of hops, we seek the optimal choice of next-hop based on its speed and inter-node distances, so as to maximize the expected route lifetime. Under a Markovian assumption on the process of speed of nodes, we show that the optimal choice of speeds attempts to equalize the lifetimes of adjacent links. A monotone variation property of the speed of relay nodes under the optimal policy is proved. These properties have been confirmed with simulations. The optimal policies and their structures can assist in enhancing the performance of existing VANET routing protocols.

Impact of Mobility on the Performance of Relaying in Ad Hoc Networks

Abstract: We consider a mobile ad hoc network consisting of three types of nodes: source, destination, and relay nodes. All the nodes are moving over a bounded region with possibly different mobility patterns. We introduce and study the notion of relay throughput, i.e. the maximum rate at which a node can relay data from the source to the destination. Our findings include the results that the relay throughput depends on the node mobility pattern only via its (stationary) node position distribution and that a node mobility pattern that results in a uniform steady-state distribution for all nodes achieves the lowest relay throughput. Random Waypoint and Random Direction mobility models in both one and in two dimensions are studied and approximate simple expressions for the relay throughput are provided. Finally, the behavior of the relay buffer occupancy is examined for the one-dimensional Random Walk, and an explicit form of its mean value is provided in the heavy-traffic case.

TCP as an Implementation of Age-Based Scheduling: Fairness and Performance

Abstract: We show that different flavors of TCP may be viewed as implementations of age-based scheduling disciplines. By parameterizing the scheduling disciplines of interest we are able to position variants of TCP in a wide spectrum having FCFS (first-come first-served) and LAS (least attained service first) as extremal policies, and including PS (processor sharing) as an intermediate case. We argue that for highly loaded systems, providing a fair bandwidth allocation among all users is secondary to ensuring network stability. So as to isolate protocol fairness from congestion effects, we therefore focus on scenarios with infinite buffers. This way, asymmetries in capacity shares are the consequences of the protocol only, and not affected by the packet loss process. The model, however, is flexible enough to include finite buffers with random packet loss as a special case (for example to capture Active Queue Management). The results are helpful in studying fairness and performance concerned with transmission protocols in communication networks. For persistent HTTP connections we study the distributions of the transmission rates and the relative fairness index under various assumptions on the file size distributions and scheduling disciplines. For infinite file sizes, we show that protocols that increase priority more than linearly with the attained service asymptotically behave similar to FCFS. In contrast, protocols with at most linearly increasing (or even decreasing) priority, with TCP's Congestion Avoidance mechanism as the most prominent example, converge to PS scheduling (even in absence of losses). When the priority is exactly linear in the attained service, such as for scalable TCP and TCP's slow start phase, the shares remain constant in between file initiations and completions.

Stability-Throughput tradeoff and routing in multi-hop wireless ad-hoc networks

Abstract: We study the throughput of multi-hop routes and stability of forwarding queues in a wireless Ad-Hoc network with random access channel. We focuse on wireless with stationary nodes, such as community wireless networks. Our main result is charactrerization of stability condition and the end-to-end throughput using the balance. We also investigate the impact of routing on end-to-end throughput and stability of intermediate nodes. We find that i) as long as the intermediate queues in the network are stable, the end-to-end throughput of a connection does not depend on the load on the intermediate nodes, ii) we showed that if the weight of a link originating from a node is set to the number of neighbors of this node, then shortest path routing maximizes the minimum probability of end-to-end packet delivery in a network of weighted fair queues with coupled servers. Numerical results are given and support the results of the analysis.

Route Lifetime based Interactive Routing in Intervehicle Mobile Ad Hoc Networks

Abstract: The main goal of this paper is to better understand the route lifetime dynamics in Intervehicle communication networks (IVC) or what we call intervehicle mobile ad hoc networks (iv-MANETs) that are a special class of MANETs but exhibit very different behavior from them. We consider the problem of finding an optimal multi-hop route between two vehicular nodes in an iv-MANET. For a given choice of the number of hops and distances between intermediate nodes, we seek the characterizing properties of choice of speeds of the intermediate nodes so as to maximize the expected lifetime of the multi-hop route. Our analytical model inherently incorporates the randomly changing speeds of nodes over time and hence the optimal choice depends on the dynamics of the stochastic process corresponding to the speed of the nodes. We suppose that for establishing a route the locations and speeds of other vehicles are known. Under a markovian assumption on the process of the speed of nodes, we show that the optimal choice of speeds attempts to equalize the lifetimes of adjacent links in a route. A monotone variation property of the speed of the intermediate nodes under the optimal policy is proved. These solution structures have been confirmed with an extensive simulation study. The heuristics and structures developed in this paper can serve in designing a new set of efficient interactive routing protocols specifically tailored for high mobility ad hoc networks and iv-MANETs in particular.

Modelling TCP Performance in Multihop 802.11 Networks with Randomly Varying Channel

Abstract: We propose a general method for modelling TCP over multihop IEEE 80211 network with time varying channel state This study is meant to provide an understanding of the effect of various parameters on TCP performance We present the general methodology via completely worked out simple examples under simplifying assumptions This analysis gives a closed form expression for TCP throughput under simplifying assumptions

Optimal control of admission to a station in a closed two queue system

Abstract: We consider a closed queueing system consisting of two stations in tandem. The controller has to make a decision on the number of customers to be admitted for service at the first station so that a long term utility function is maximized. We study the nature of optimal policy for some classes of utility function and transition probability structures. This model can be used to solve many practical closed queueing system problems, like node activation in a rechargeable sensor network. We show that, depending on the number of servers at the various stations, the optimal policy may or may not be greedy.

Sojourn times in (discrete) time shared systems and their continuous time limits

Abstract: We consider two classes of preemptive processor sharing scheduling policies in which the instantaneous weight given to a customer depends on a) the amount of service already imparted to the customer (Age-based scheduling), or b) the amount of service yet to be imparted to the customer (Residual Processing Time, RPT, based scheduling). We analyze the system for the mean sojourn time of a tagged customer conditioned on its service requirement. The main contribution of this article are:i) We decompose the sojourn time of a customer into two parts: a) the contribution of the descendants of the customer, and b) the contribution of the jobs (and their descendants) which the customer sees on arrival. For the preemptive system under consideration, it is shown that the behavior of the mean sojourn time for large values of service requirement is determined only by the first term above. We provide a closed form expression for this component of the sojourn time for general Age-based and RPT-based scheduling disciplines.iii) If the weight assigned to a customer with an age x units is xα for some α, we show that the behavior of mean sojourn time conditioned on service requirement is asymptotically linear for all 0 ≤ α ≤ 1. Moreover, this asymptotic slope is same for 0 ≤ α

Tail equivalence for some time-shared systems

Abstract: Many of recent studies have proved the tail equivalence result for Egalitarian Processor Sharing system: [EQUATION], where B (resp. V) is service requirement (resp. sojourn time) of a customer; for PS, g = 1 - ρ. In this paper, we consider time-shared systems in which the server capacity is shared by existing customers in proportion to (dynamic) weights assigned to customers. We consider two systems, 1) in which the weight of a customer depends on it Age (attained service), and 2) in which the weight depends on the residual processing time (RPT). We allow for a parameterized family of weight functions such that the weight associated with a customer that has received a service (or, has a RPT) of x units is ω(x) = xα for some -∞

A Structural Property of Solutions to Path Optimization Problems in Random Access Networks

Abstract: The inherent nature of the physical setup and transmission mechanism in wireless ad hoc networks with random channel access, results in correlation between the link metrics of adjacent links, when considering path optimization problems. We identify a special structure inherent to the solution of Dynamic Programming (DP) problem arising in such an optimization over paths. According to this structure, the optimal policy tries to equalize the link metrics of adjacent links in a multi-hop route. We validate this structural property with simulations.

A direct approach to sojourn times in a busy period of an M/M/1 queue

Abstract: In this paper we present a direct approach to obtaining joint distributions of various quantities of interest in a busy period in an M/M/1 queue. These quantities are: the sojourn times and waiting times of all the customers in the busy period, the busy period length and the number of customers served in a busy period. Since the evolution of the total workload process between two successive customer arrivals is deterministic, this work gives statistic of the complete evolution of the workload process within a busy period.