Optimal admission control in circuit-switched multihop radio networks

Abstract

In this paper we address admission control in circuitswitched multihop radio networks. Our problem formulation is based on the multiple service, multiple resource (MSMR) model developed by Jordan and Varaiya [1,2]. They have shown that, under a reasonable set of assumptions, coupled with the requirement of a coordinate convex state space [3], a product-form stationary distribution is obtained for the system state. In such systems, the control policy is implemented by restricting the admissible state space to the coordinate convex subspace that results in the optimum value of the desired performance index.We address the computational evaluation of the performance measures of interest, and we discuss a descentsearch procedure for the determination of a good control policy. Computational results demonstrate that little performance improvement is achieved by means of admissioncontrol schemes unless the performance measure associates different weights with different types of calls.

Ordinal optimization for a class of deterministic and stochastic discrete resource allocation problems

“…Even though A1) limits the applicability of the approach to a class of resource allocation problems, it is also true that this class includes a number of interesting problems. Examples include: 1) buffer allocation in parallel queueing systems where the blocking probability is a function of the number of buffer slots assigned to each server (for details, see Section V); note, however, that A1) does not hold in the case of a tandem queueing system; 2) cellular systems where the call loss probability of each cell depends only on the number of channels assigned to each cell; and 3) scheduling packet transmissions in a mobile radio network, where the resources are the time slots in a transmission frame (see [5] and [18]).…”

“…If, however, this is not the case and is determined by arbitrarily breaking a tie, then we simply leave this index unchanged as long as for which implies that all values remain unchanged. Interpretation of (14)- (18): Before proceeding with a detailed analysis of the processes for each let us provide an informal description and interpretation of the full dynamic allocation scheme (14)- (18). Looking at (15), identifies the user "most sensitive" to the removal of a resource among those users in the set while in (16), identifies the user who is "least sensitive."…”

“…Then, (14) forces a natural exchange of resources from the least to the most sensitive user at the th step of this process, provided the quantity is strictly positive (an interpretation of is provided below). Otherwise, the allocation is unaffected, but the user with index is removed from the set through (18). Thus, as the process evolves, users are gradually removed from this set.…”

“…We begin by establishing in Lemma 3.1 below a number of properties that the sequences and in (14) and (18), respectively, satisfy. Based on these properties, we will show that where converges to a globally optimal allocation.…”

“…A classic example is the buffer (or kanban) allocation problem in queueing models of manufacturing systems [10], [20], where a fixed number of buffers (or kanban) must be allocated over a fixed number of servers to optimize some performance metric. Another example is the transmission scheduling problem in radio networks [5], [18], where a fixed number of time slots forming a "frame" must be allocated over several nodes. In the basic model we will consider in this paper, there are identical resources to be allocated over user classes so as to optimize some system performance measure (objective function).…”