For realistic scale-free networks, we investigate the traffic properties of stochastic routing inspired by a zero-range process known in statistical physics. By parameters @math and @math , this model controls degree-dependent hopping of packets and forwarding of packets with higher performance at more busy nodes. Through a theoretical analysis and numerical simulations, we derive the condition for the concentration of packets at a few hubs. In particular, we show that the optimal @math and @math are involved in the trade-off between a detour path for @math ; In the low-performance regime at a small @math , the wandering path for @math and @math is small, neither the wandering long path with short wait trapped at nodes ( @math ), nor the short hopping path with long wait trapped at hubs ( @math ) is advisable. A uniformly random walk ( @math ) yields slightly better performance. We also discuss the congestion phenomena in a more complicated situation with packet generation at each time step.
Other routing schemes @cite_20 @cite_18 @cite_17 have also been considered, taking into account lengths of both the routing path and of the queue. In a deterministic model @cite_18 , a forwarding node @math is chosen among neighbors @math by minimizing the quantity @math with a weight @math , @math denoting the distance from @math to the terminal node. Since we must solve the optimization problems, these models @cite_21 @cite_18 are not suitable for wireless or ad hoc communication networks. Thus, stochastic routing methods using only local information are potentially promising. In a stochastic model @cite_17 , @math is chosen at random, and a packet at the top of its queue is sent with probability @math or refused with probability @math as a nondecreasing function of the queue length @math . This model is simplified by the assumption of a constant arrival rate of packets, for analyzing the critical point of traffic congestion in a mean-field equation @cite_17 .
@cite_18 @cite_21 @cite_20 @cite_17
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This paper is meant to be an illustration of the use of stochastic geometry for analyzing the performance of routing in large wireless ad hoc (mobile or mesh) networks. In classical routing strategies used in such networks, packets are transmitted on a pre-defined route that is usually obtained by a shortest-path routing protocol. In this paper we review some recent ideas concerning a new routing technique which is opportunistic in the sense that each packet at each hop on its (specific) route from an origin to a destination takes advantage of the actual pattern of nodes that captured its recent (re)transmission in order to choose the next relay. The paper focuses both on the distributed algorithms allowing such a routing technique to work and on the evaluation of the gain in performance it brings compared to classical mechanisms. On the algorithmic side, we show that it is possible to implement this opportunistic technique in such a way that the current transmitter of a given packet does not need to know its next relay a priori, but the nodes that capture this transmission (if any) perform a self-selection procedure to choose the packet relay node and acknowledge the transmitter. We also show that this routing technique works well with various medium access protocols (such as Aloha, CSMA, TDMA). Finally, we show that the above relay self-selection procedure can be optimized in the sense that it is the node that optimizes some given utility criterion (e.g. minimize the remaining distance to the final destination), which is chosen as the relay. The performance evaluation part is based on stochastic geometry and combines simulation as analytical models. The main result is that such opportunistic schemes very significantly outperform classical routing schemes when properly optimized and provided at least a small number of nodes in the network know their geographical positions exactly. We study wireless ad hoc networks with a large number of nodes. We first focus on a network of n immobile nodes, each with a destination node chosen in random. We develop a scheme under which, in the absence of fading, the network can provide each node with a traffic rate spl lambda sub 1 (n)=K sub 1 (nlog n) sup -1 2 . This result was first shown in J. Hightower and G. Borriello (2001) under a similar setting, however the proof presented here is shorter and uses only basic probability tools. We then proceed to show that, under a general model of fading, each node can send data to its destination with a rate spl lambda sub 2 (n)=K sub 2 n sup -1 sup 2 (log n) sup -3 2 . Next, we extend our formulation to study the effects of node mobility. We first develop a simple scheme under which each of the a mobile nodes can send data to a randomly chosen destination node with a rate spl lambda sub 3 (n)=K sub 3 n sup -1 2 (log n) sup -3 2 , and with a fixed upper bound on the packet delay d sub max that does not depend on n. We subsequently develop a scheme under which each of the nodes can send data to its destination with a rate spl lambda sub 4 (n)=K sub 4 n sup (d-1) 2 (log n) sup -5 2 provided that nodes are willing to tolerate packet delays smaller than d sub max (n)<K sub 5 n sup d , where 0<d<1. With both schemes, a general model of fading is assumed. In addition, nodes require no global topology or routing information, and only need to coordinate locally. The above results hold for an appropriate choice of values for the constants K sub i , and with probability approaching 1 as the number of nodes n approaches infinity. Existing position-based unicast routing algorithms which forward packets in the geographic direction of the destination require that the forwarding node knows the positions of all neighbors in its transmission range. This information on direct neighbors is gained by observing beacon messages each node sends out periodically. Due to mobility, the information that a node receives about its neighbors becomes outdated, leading either to a significant decrease in the packet delivery rate or to a steep increase in load on the wireless channel as node mobility increases. In this paper, we propose a mechanism to perform position-based unicast forwarding without the help of beacons. In our contention-based forwarding scheme (CBF) the next hop is selected through a distributed contention process based on the actual positions of all current neighbors. For the contention process, CBF makes use of biased timers. To avoid packet duplication, the first node that is selected suppresses the selection of further nodes. We propose three suppression strategies which vary with respect to forwarding efficiency and suppression characteristics. We analyze the behavior of CBF with all three suppression strategies and compare it to an existing greedy position-based routing approach by means of simulation with ns-2. Our results show that CBF significantly reduces the load on the wireless channel required to achieve a specific delivery rate compared to the load a beacon-based greedy forwarding strategy generates. We consider packet scheduling in a network providing differentiated services, where each packet is assigned a value. We study various queueing models for supporting QoS (Quality of Service). In the nonpreemptive model, packets accepted to the queue will be transmitted eventually and cannot be dropped. The FIFO preemptive model allows packets accepted to the queue to be preempted (dropped) prior to their departure, while ensuring that transmitted packets are sent in the order of arrival. In the bounded delay model, packets must be transmitted before a certain deadline, otherwise it is lost (while transmission ordering is allowed to be arbitrary). In all models the goal of the buffer policy is to maximize the total value of the accepted packets.Let α be the ratio between the maximal and minimal value. For the non-preemptive model we derive a Θ(log &alpha) competitive ratio, both exhibiting a buffer policy and a general lower bound. For the interesting case of two distinct values, we give an 2α--1 α competitive buffer policy, which exactly matches the lower bound. We also analyze a RED-like policy and derive its competitive ratio, which is approximately 2α--0.5 α for two values and Θ(log α) for multiple values. In addition we improve the previous known lower and upper bounds of the Fixed Partition and Flexible Partition policies.For the FIFO preemptive model, we improve the general lower bound and show a tight bound for the special case of queue size 2. We prove that the bounded delay model with uniform delay 2 is equivalent to a modified FIFO preemptive model with queue size 2. We then give improved upper and lower bounds on the 2-uniform bounded delay model. We also give lower bound for the 2-variable bounded delay model, which matches the previously known upper bound.