We study the problem of assigning @math identical servers to a set of @math parallel queues in a time-slotted queueing system. The connectivity of each queue to each server is randomly changing with time; each server can serve at most one queue and each queue can be served by at most one server during each time slot. Such a queueing model has been used in addressing resource allocation problems in wireless networks. It has been previously proven that Maximum Weighted Matching (MWM) is a throughput-optimal server assignment policy for such a queueing system. In this paper, we prove that for a system with i.i.d. Bernoulli packet arrivals and connectivities, MWM minimizes, in stochastic ordering sense, a broad range of cost functions of the queue lengths such as total queue occupancy (which implies minimization of average queueing delays). Then, we extend the model by considering imperfect services where it is assumed that the service of a scheduled packet fails randomly with a certain probability. We prove that the same policy is still optimal for the extended model. We finally show that the results are still valid for more general connectivity and arrival processes which follow conditional permutation invariant distributions.
In contrast to the single-server system (where LCQ was both throughput-optimal and delay-optimal), in MQMS-Type1 system the MW policy is not necessarily delay-optimal. More specifically, in @cite_29 it was also shown that although MW policy is throughput-optimal, even for a system with i.i.d. Bernoulli arrivals and connectivity processes, MW policy in its general form, is not delay-optimal.
@cite_29
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This paper proposes a new class of online policies for scheduling in input-buffered crossbar switches. Given an initial configuration of packets at the input buffers, these policies drain all packets in the system in the minimal amount of time provided that there are no further arrivals. These policies are also throughput optimal for a large class of arrival processes which satisfy strong-law of large numbers. We show that it is possible for policies in our class to be throughput optimal even if they are not constrained to be maximal in every time slot. Most algorithms for switch scheduling take an edge based approach; in contrast, we focus on scheduling (a large enough set of) the most congested ports. This alternate approach allows for lower-complexity algorithms, and also requires a non-standard technique to prove throughput-optimality. One algorithm in our class, Maximum Vertex-weighted Matching (MVM) has worst-case complexity similar to Max-size Matching, and in simulations shows slightly better delay performance than Max-(edge)weighted-Matching (MWM). We consider a general single-server multiclass queueing system that incurs a delay cost Ck(Tk) for each class k job that resides Tk units of time in the system. This paper derives a scheduling policy that minimizes the total cumulative delay cost when the system operates during a finite time horizon. Denote the marginal delay cost function and the (possibly non-stationary) average processing time of class k by ck = C'k and 1 uk, respectively, and let ak(t) be the "age" or time that the oldest class k job has been waiting at time t. We call the scheduling policy that at time t serves the oldest waiting job of that class k with the highest index uk(t)ck(ak(t)), the generalized cu rule. As a dynamic priority rule that depends on very little data, the generalized cu rule is attractive to implement. We show that, with nondecreasing convex delay costs, the generalized cu rule is asymptotically optimal if the system operates in heavy traffic and give explicit expressions for the associated performance characteristics: the delay (throughput time) process and the minimum cumulative delay cost. The optimality result is robust in that it holds for a countable number of classes and several homogeneous servers in a nonstationary, deterministic or stochastic environment where arrival and service processes can be general and interdependent. Network capacity region of multi-queue multi-server queueing system with random connectivities and stationary arrival processes is studied in this paper. Specifically, the necessary and sufficient conditions for the stability of the system are derived under general arrival processes with finite first and second moments. In the case of stationary arrival processes, these conditions establish the network capacity region of the system. It is also shown that AS LCQ (Any Server Longest Connected Queue) policy stabilizes the system when it is stabilizable. Furthermore, an upper bound for the average queue occupancy is derived for this policy. In this correspondence, we consider a cellular network consisting of a base station and N receivers. The channel states of the receivers are assumed to be identical and independent of each other. The goal is to compare the throughput of two different scheduling policies (a queue-length-based (QLB) policy and a greedy policy) given an upper bound on the queue overflow probability or the delay violation probability. We consider a multistate channel model, where each channel is assumed to be in one of L states. Given an upper bound on the queue overflow probability or an upper bound on the delay violation probability, we show that the total network throughput of the (QLB) policy is no less than the throughput of the greedy policy for all N. We also obtain a lower bound on the throughput of the (QLB) policy. For sufficiently large N, the lower bound is shown to be tight, strictly increasing with N, and strictly larger than the throughput of the greedy policy. Further, for a simple multistate channel model-ON-OFF channel, we prove that the lower bound is tight for all N