Michael M. Markou

Optimization of discrete event system parameters using SFM-based infinitesimal perturbation analysis estimates

This paper deals with the problem of optimizing the performance of a discrete event system (DES) using infinitesimal perturbation analysis (IPA) estimates obtained from a stochastic fluid model (SFM). In order to better approximate the behavior of the DES, we propose a special case of SFM where the arrival and service processes are modeled by piecewise constant ON/OFF sources. The proposed SFM however violates some of the assumptions made in Cassandras, C. G., et al (2002) and as a result the sample derivatives no longer exist. However, using the proposed SFM, we obtain the left and right sided sample derivative estimates. This paper investigates the implementation of various IPA estimates that have been derived based on a stochastic fluid model (SFM) for the optimization of parameters of a discrete event system (DES). In this paper we investigate gradient based and subgradient optimization methods. As shown in this paper, for many scenarios all algorithms have comparable results however, in some cases subgradient optimization produces better results.

Perturbation analysis of stochastic fluid models with respect to the fluid arrival process

The deployment of network applications (e.g., multimedia and other real time applications) has put extra pressure on network scarce resources (bandwidth and buffers) thus generating a need for effective resource allocation and management. In this paper we adopt a stochastic fluid model (SFM) framework and derive sensitivity estimators for three performance measures of interest (workload, throughput and loss volume) with respect to the fluid inflow process parameters. The motivation is to use the sensitivity estimators for dynamic control and optimisation of the systems performance. Subsequently these estimators are evaluated based on data observed from a single sample path of the discrete-event system and are used to dynamically control the input process to the system allowing the network to work continuously at an optimal or near optimal point. The proposed analysis naturally leads to a distributed algorithm for evaluating the propagation of perturbations in a network (e.g., due to changes in the buffer size of upstream nodes).

On Evaluating SFM-Based Infinitesimal Perturbation Analysis Estimates From Discrete Event System Data

This paper investigates the evaluation of infinitesimal perturbation analysis (IPA) estimates that have been derived based on a stochastic fluid model (SFM) using data observed from the sample path of a discrete event system (DES). First, we show that a straightforward implementation of the SFM-based IPA estimates may yield biased estimates when the data are obtained from the actual DES. Then, in order to better approximate the sample path of the DES, we propose a special case of SFM where the arrival and service processes are modeled by piecewise constant on/off sources. The proposed SFM violates some of the assumptions made in [1]-[4] , and, as a result, the sample derivatives no longer exist. However, using the proposed SFM, we obtain the left and right sided sample derivative estimates. As shown in this paper, the sided sample derivatives are much better in approximating the required derivatives compared to the straightforward implementation of the SFM-based IPA estimates.

GEN02-6: Dynamic Control and Optimization of Buffer Size in Multiclass Wireless Networks

Third generation (3G) wireless networks enable the deployment of real time applications that put extra pressure on network scarce resources (bandwidth and buffers) thus generating a need for effective resource allocation and management. This work studies the problem of dynamic control and optimization of buffer thresholds in wireless networks. Based on a stochastic fluid model (SFM), this paper derives infinitesimal perturbation analysis (IPA) estimators of the sensitivity of some performance measure of interest with respect to the control parameter. Subsequently these estimators are evaluated based on data observed from the sample path of the system and are used to dynamically control the threshold allowing the network to work continuously at an optimal or near optimal point.

Dynamic control and optimization of buffer size for short message transfer in GPRS-UMTS networks

This work focuses on the problem of dynamically determining the optimal buffer threshold for message transferring services (SMS, MMS) in GPRS-UMTS networks. An infinitesimal perturbation analysis (IPA), based on stochastic fluid models (SFM) is used to obtain sensitivity estimates of the performance measure of interest with respect to the control parameter and the near-optimal buffer threshold is obtained by using stochastic approximation techniques. As a result, these approaches are used continuously to adjust the buffer size when the traffic condition changes.

On-line optimization and control of the buffer sizes in a cellular network communication system

Motivated by the cellular model paradigm, this paper develops a distributed on-line algorithm for determining the values of the control parameters (in this case, the buffer sizes) that optimize some predefined performance metrics of interest (e.g. average queue length, average loss probability). Stochastic Fluid Model (SFM) framework is adopted to model the queuing systems. Using this framework, we derive Infinitesimal Perturbation Analysis (IPA) estimates of the performance metrics of interest with respect to the control parameters. These estimates are shown to be unbiased which means that they can be used in a Stochastic Approximation (SA) based algorithm to drive the system to the optimal solution. Subsequently, these estimators are evaluated based on data observed from the sample path of the “real” system and used in the SA algorithm to dynamically control the buffer sizes in a distributed manner, allowing the network to work continuously at an optimal point. The correctness of the algorithm is verified through simulations using a network model of two tightly coupled nodes. The contribution of this paper is that it derives the fluid-based IPA algorithms for the specific communication network investigated, which can eventually lead to distributed protocols for controlling the buffer size of the nodes of a cellular network to optimize the overall networks performance.

Distributed Dynamic Resource Allocation in Tandem Networks

Considering a tandem network of queues (each representing the buffer in a router) our objective is to allow each individual queue to dynamically control its own parameters (in this paper the buffer size) using only information available locally and from neighboring nodes. For each node we adopt control approaches that are based on Infinitesimal Perturbation Analysis (IPA) estimates of certain performance measures. In this family of approaches we investigate collaboration schemes that can lead us to global optimal (or near optimal) solutions. The contribution of the paper is the design of a simple protocol that allows neighboring nodes to collaboratively exchange information in order to converge to a global optimal solution.