Concave Switching in Single and Multihop Networks

Switched queueing networks model wireless networks, input queued switches and numerous other networked communications systems. For single-hop networks, we consider a {($\alpha,g$)-switch policy} which combines the MaxWeight policies with bandwidth sharing networks -- a further well studied model of Internet congestion. We prove the maximum stability property for this class of randomized policies. Thus these policies have the same first order behavior as the MaxWeight policies. However, for multihop networks some of these generalized polices address a number of critical weakness of the MaxWeight/BackPressure policies. For multihop networks with fixed routing, we consider the Proportional Scheduler (or (1,log)-policy). In this setting, the BackPressure policy is maximum stable, but must maintain a queue for every route-destination, which typically grows rapidly with a network's size. However, this proportionally fair policy only needs to maintain a queue for each outgoing link, which is typically bounded in number. As is common with Internet routing, by maintaining per-link queueing each node only needs to know the next hop for each packet and not its entire route. Further, in contrast to BackPressure, the Proportional Scheduler does not compare downstream queue lengths to determine weights, only local link information is required. This leads to greater potential for decomposed implementations of the policy. Through a reduction argument and an entropy argument, we demonstrate that, whilst maintaining substantially less queueing overhead, the Proportional Scheduler achieves maximum throughput stability.Comment: 28 page

Induced burstiness in generalized processor sharing queues with long-tailed traffic flows

We analyze the queueing behavior of long-tailed traffic flows under the Generalized Processor Sharing (GPS) discipline. GPS-based scheduling algorithms, such as Weighted Fair Queueing, play a major role in achieving differentiated quality-of-service in integrated-services networks. We prove that, in certain scenarios, a flow may be strongly affected by the activity of `heavier'-tailed flows, and may inherit their traffic characteristics, causing induced burstiness. This phenomenon contrasts with previous results which show that, under certain conditions, an individual flow with long-tailed traffic characteristics is effectively served at a constant rate. In particular, the flow is then essentially immune from excessive activity of flows with `heavier'-tailed traffic characteristics. The sharp dichotomy in qualitative behavior illustrates the crucial importance of the weight parameters in protecting individual flows

Large Deviations and the Generalized Processor Sharing Scheduling: Upper and Lower Bounds Part I: Two-Queue Systems

We prove asymptotic upper and lower bounds on the asymptotic decay rate of per-session queue length tail distributions for a single constant service rate server queue shared by multiple sessions with the generalized processor sharing (GPS) scheduling discipline. The simpler case of a GPS system with only two queues needs special attention, as under this case, it is shown that the upper bounds and lower boundsmatch, thus yielding exact bounds. This result is established in this part (Part I) of the paper. The general case is much more complicated, and is treated separately in Part II of the paper [42], where tight upper and lower bound results are proved by examining the dynamics of bandwidth sharing nature of GPS scheduling. The proofs use sample-path large deviation principle and are based on some recent large deviation results for a single queue with a constant service rate server. These results have implications in call admission control for high-speed communication networks

Frequency scaling in multilevel queues

In this paper, we study a variant of PS+PS multilevel scheduling, which we call the PS+IS queue. Specifically, we use Processor Sharing (PS) at both queues, but with linear frequency scaling on the second queue, so that the latter behaves like an Infinite Server (IS) queue. The goals of the system are low response times for small jobs in the first queue, and reduced power consumption for large jobs in the second queue. The novelty of our model includes the frequency scaling at the second queue, and the batch arrival process at the second queue induced by the busy period structure of the first queue which has strictly higher priority. We derive a numerical solution for the PS+IS queueing system in steady-state, and then study its properties under workloads obtained from fitting of TCP flow traces. The simulation results confirm the

Problems related to the integration of fault tolerant aircraft electronic systems

Problems related to the design of the hardware for an integrated aircraft electronic system are considered. Taxonomies of concurrent systems are reviewed and a new taxonomy is proposed. An informal methodology intended to identify feasible regions of the taxonomic design space is described. Specific tools are recommended for use in the methodology. Based on the methodology, a preliminary strawman integrated fault tolerant aircraft electronic system is proposed. Next, problems related to the programming and control of inegrated aircraft electronic systems are discussed. Issues of system resource management, including the scheduling and allocation of real time periodic tasks in a multiprocessor environment, are treated in detail. The role of software design in integrated fault tolerant aircraft electronic systems is discussed. Conclusions and recommendations for further work are included

A generalized processor sharing approach to flow control in integrated services networks : the single server case

Caption title.Includes bibliographical references (p. 47-48).Research supported by a Vinton Hayes Fellowship.Abhay K. Parekh and Robert G. Gallager