2 research outputs found
Optimal Multi-Server Allocation to Parallel Queues With Independent Random Queue-Server Connectivity
We investigate an optimal scheduling problem in a discrete-time system of L
parallel queues that are served by K identical, randomly connected servers.
Each queue may be connected to a subset of the K servers during any given time
slot. This model has been widely used in studies of emerging 3G/4G wireless
systems. We introduce the class of Most Balancing (MB) policies and provide
their mathematical characterization. We prove that MB policies are optimal; we
define optimality as minimization, in stochastic ordering sense, of a range of
cost functions of the queue lengths, including the process of total number of
packets in the system. We use stochastic coupling arguments for our proof. We
introduce the Least Connected Server First/Longest Connected Queue (LCSF/LCQ)
policy as an easy-to-implement approximation of MB policies. We conduct a
simulation study to compare the performance of several policies. The simulation
results show that: (a) in all cases, LCSF/LCQ approximations to the MB policies
outperform the other policies, (b) randomized policies perform fairly close to
the optimal one, and, (c) the performance advantage of the optimal policy over
the other simulated policies increases as the channel connectivity probability
decreases and as the number of servers in the system increases.Comment: 53 single-column pages, 8 figure
Explicit Characterization of Stability Region for Stationary Multi-Queue Multi-Server Systems
In this paper, we characterize the network stability region (capacity region)
of multi-queue multi-server (MQMS) queueing systems with stationary channel
distribution and stationary arrival processes. The stability region is
specified by a finite set of linear inequalities. We first show that the
stability region is a polytope characterized by the finite set of its facet
defining hyperplanes. We explicitly determine the coefficients of the linear
inequalities describing the facet defining hyperplanes of the stability region
polytope. We further derive the necessary and sufficient conditions for the
stability of the system for general arrival processes with finite first and
second moments. For the case of stationary arrival processes, the derived
conditions characterize the system stability region. Furthermore, we obtain an
upper bound for the average queueing delay of Maximum Weight (MW) server
allocation policy which has been shown in the literature to be a throughput
optimal policy for MQMS systems. Using a similar approach, we can characterize
the stability region for a fluid model MQMS system. However, the stability
region of the fluid model system is described by an infinite number of linear
inequalities since in this case the stability region is a convex surface. We
present an example where we show that in some cases depending on the channel
distribution, the stability region can be characterized by a finite set of
non-linear inequalities instead of an infinite number of linear inequalities.Comment: 35 pages, 16 figure