User-level performance of channel-aware scheduling algorithms in wireless data networks

Channel-aware scheduling strategies, such as the Proportional Fair algorithm for the CDMA 1xEV-DO system, provide an effective mechanism for improving throughput performance in wireless data networks by exploiting channel fluctuations. The performance of channel-aware scheduling algorithms has mostly been explored at the packet level for a static user population, often assuming infinite backlogs. In the present paper, we focus on the performance at the flow level in a dynamic setting with random finite-size service demands. We show that in certain cases the user-level performance may be evaluated by means of a multi-class Processor-Sharing model where the total service rate varies with the total number of users. The latter model provides explicit formulas for the distribution of the number of active users of the various classes, the mean response times, the blocking probabilities, and the mean throughput. In addition we show that, in the presence of channel variations, greedy, myopic strategies which maximize throughput in a static scenario, may result in sub-optimal throughput performance for a dynamic user configuration and cause potential instability effects

Dynamic rate control algorithms for HDR throughput optimization

The relative delay tolerance of data applications, together with the bursty traffic characteristics, opens up the possibility for scheduling transmissions so as to optimize throughput. A particularly attractive approach, in fading environments, is to exploit the variations in the channel conditions, and transmit to the user with the currently `best' channel. We show that the `best' user may be identified as the maximum-rate user when the feasible rates are weighed with some appropriately determined coefficients. Interpreting the coefficients as shadow prices, or reward values, the optimal strategy may thus be viewed as a revenue-based policy, which always assigns the transmission slot to the user yielding the maximum revenue. Calculating the optimal revenue vector directly is a formidable task, requiring detailed information on the channel statistics. Instead, we present adaptive algorithms for determining the optimal revenue vector on-line in an iterative fashion, without the need for explicit knowledge of the channel behavior. Starting from an arbitrary initial vector, the algorithms iteratively adjust the reward values to compensate for observed deviations from the target throughput ratios. The algorithms are validated through extensive numerical experiments. Besides verifying long-run convergence, we also examine the transient performance, in particular the rate of convergence to the optimal revenue vector. The results show that the target throughput ratios are tightly maintained, and that the algorithms are well able to track sudden changes in the channel conditions or throughput targets

A reduced-load equivalence for generalised processor sharing networks with heavy-tailed input flows

We consider networks where traffic is served according to the Generalised Processor Sharing (GPS) principle. GPS-based scheduling algorithms are considered important for providing differentiated quality of service in integrated-services networks. We are interested in the workload of a particular flow~$i$ at the bottleneck node on its path. Flow $i$ is assumed to have long-tailed traffic characteristics. We distinguish between two traffic scenarios, (i) flow~$i$ generates instantaneous traffic bursts and (ii) flow $i$ generates traffic according to an on/off process. In addition, we consider two configurations of feed-forward networks. First we focus on the situation where other flows join the path of flow~$i$. Then we extend the model by adding flows which can branch off at any node, with cross traffic as a special case. We prove that under certain conditions the tail behaviour of the workload distribution of flow~$i$ is equivalent to that in a {em two-node tandem network where flow~$i$ is served in isolation at {em constant rates. These rates only depend on the traffic characteristics of the other flows through their average rates. This means that the results do not rely on any specific assumptions regarding the traffic processes of the other flows. In particular, flow~$i$ is not affected by excessive activity of flows with `heavier-tailed' traffic characteristics. This confirms that GPS has the potential to protect individual flows against extreme behaviour of other flows, while obtaining substantial multiplexing gains

A reduced-load equivalence for generalised processor sharing networks with heavy-tailed input flows

We consider networks where traffic is served according to the Generalised Processor Sharing (GPS) principle. GPS-based scheduling algorithms are considered important for providing differentiated quality of service in integrated-services networks. We are interested in the workload of a particular flow~$i$ at the bottleneck node on its path. Flow $i$ is assumed to have long-tailed traffic characteristics. We distinguish between two traffic scenarios, (i) flow~$i$ generates instantaneous traffic bursts and (ii) flow $i$ generates traffic according to an on/off process. In addition, we consider two configurations of feed-forward networks. First we focus on the situation where other flows join the path of flow~$i$. Then we extend the model by adding flows which can branch off at any node, with cross traffic as a special case. We prove that under certain conditions the tail behaviour of the workload distribution of flow~$i$ is equivalent to that in a {em two-node tandem network where flow~$i$ is served in isolation at {em constant rates. These rates only depend on the traffic characteristics of the other flows through their average rates. This means that the results do not rely on any specific assumptions regarding the traffic processes of the other flows. In particular, flow~$i$ is not affected by excessive activity of flows with `heavier-tailed' traffic characteristics. This confirms that GPS has the potential to protect individual flows against extreme behaviour of other flows, while obtaining substantial multiplexing gains

Queuing delays in randomized load balanced networks

Valiant’s concept of Randomized Load Balancing (RLB), also promoted under the name ‘two-phase routing’, has previously been shown to provide a cost-effective way of implementing overlay networks that are robust to dynamically changing demand patterns. RLB is accomplished in two steps; in the first step, traffic is randomly distributed across the network, and in the second step traffic is routed to the final destination. One of the benefits of RLB is that packets experience only a single stage of routing, thus reducing queueing delays associated with multi-hop architectures. In this paper, we study the queuing performance of RLB, both through analytical methods and packet-level simulations using ns2 on three representative carrier networks. We show that purely random traffic splitting in the randomization step of RLB leads to higher queuing delays than pseudo-random splitting using, e.g., a round-robin schedule. Furthermore, we show that, for pseudo-random scheduling, queuing delays depend significantly on the degree of uniformity of the offered demand patterns, with uniform demand matrices representing a provably worst-case scenario. These results are independent of whether RLB employs priority mechanisms between traffic from step one over step two. A comparison with multi-hop shortest-path routing reveals that RLB eliminates the occurrence of demand-specific hot spots in the network

Robustness of power-law behavior in cascading line failure models

Inspired by reliability issues in electric transmission networks, we use a probabilistic approach to study the occurrence of large failures in a stylized cascading line failure model. Such models capture the phenomenon where an initial line failure potentially triggers massive knock-on effects. Under certain critical conditions, the probability that the number of line failures exceeds a large threshold obeys a power-law distribution, a distinctive property observed in empiric blackout data. In this paper, we examine the robustness of the power-law behavior by exploring under which conditions this behavior prevails