Worst-Case Deterministic Delay Bounds for Arbitrary Weighted Generalized Processor Sharing Schedulers

Abstract

Generalized Processor Sharing (GPS) is realized as the most important ideal fluid scheduling discipline in guaranteed QoS networks. The well-known problem of GPS-based rate-proportional servers is the bandwidth delay coupling which leads to inefficient resource utilization. In this paper we introduce the concept of non rate-proportional (or arbitrary) weighting of sessions in GPS systems. Such an approach in a GPS node of network constrained by leaky buckets can handle bandwidth and delay parameters independently, thus allowing better utilization of network resources. Moreover, we show that even under the traditional bandwidth delay coupled system (rate-proportional weighting) it is possible to determine tighter delay bounds of sessions than that of presented in earlier papers. A numerically inexpensive algorithm, which works in any arbitrary weighted GPS system is also presented for computing delay bounds. Besides the analytical work numerical examples are also shown. 1 a session is said to be backlogged if there are some data in its queue 2 an interval the server is continuously working

QoS Mechanisms for the MAC Protocol of IEEE 802.11 WLANs

“…As mentioned above, a tight bound is found in [2,14], and [20], for the maximum delay that a leaky-bucket constrained session experiences in a GPS server. The relevant bound is tighter than that found in [17], as it explicitly takes into account that the bandwidth unused by some sessions will be redistributed among the backlogged sessions proportionally to their respective weights φ i .…”

“…Let T j (t) denote the time at which A j (0, T j (t)) = W j (0, t), i.e., the time at which the amount of traffic received was equal to the amount of traffic that has been serviced by time t. If we let D j (t) denote the delay experienced by the traffic completing service at time t, then D j (t) = t − T j (t). It is partly shown in [20], that, in the worst case when the traffic source is greedy, the following equality holds:…”

“…Recently, an expression has been found in [2,14,20], for the tight delay bounds that characterize GPS systems with leaky-bucket constrained input traffic sources, and CAC algorithms have been proposed based on such bounds. Unfortunately, the previous algorithms do not take full advantage of the available information.…”

End-to-end delay bound calculation in generalized processor sharing networks

“…Note that these results hold for the case when session weights are set in proportional to their bandwidth demands (+i N pi), which is the class of rate-proportional servers (RPPS). We propose the use of arbitrary weighting of sessions to achieve bandwidth-delay decoupling [7,81, despite the fact that it complicates the task of delay bound calculation and resource assignment both in single server and networking environment.…”

“…(4) According to this result, the service function of a given session under the all greedy scenario is its service curve, and it can be used as a lower bound on the session's received service in any other scenarios. Thus, this service function is a basis for the worst case bounds computation for the single node case [7] and will be of crucial importance for the multiple node case too.…”