Exponential penalty function control of loss networks

We introduce penalty-function-based admission control policies to approximately maximize the expected reward rate in a loss network. These control policies are easy to implement and perform well both in the transient period as well as in steady state. A major advantage of the penalty approach is that it avoids solving the associated dynamic program. However, a disadvantage of this approach is that it requires the capacity requested by individual requests to be sufficiently small compared to total available capacity. We first solve a related deterministic linear program (LP) and then translate an optimal solution of the LP into an admission control policy for the loss network via an exponential penalty function. We show that the penalty policy is a target-tracking policy--it performs well because the optimal solution of the LP is a good target. We demonstrate that the penalty approach can be extended to track arbitrarily defined target sets. Results from preliminary simulation studies are included.Comment: Published at http://dx.doi.org/10.1214/105051604000000936 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Balanced routing of random calls

We consider an online network routing problem in continuous time, where calls have Poisson arrivals and exponential durations. The first-fit dynamic alternative routing algorithm sequentially selects up to $d$ random two-link routes between the two endpoints of a call, via an intermediate node, and assigns the call to the first route with spare capacity on each link, if there is such a route. The balanced dynamic alternative routing algorithm simultaneously selects $d$ random two-link routes, and the call is accepted on a route minimising the maximum of the loads on its two links, provided neither of these two links is saturated. We determine the capacities needed for these algorithms to route calls successfully and find that the balanced algorithm requires a much smaller capacity. In order to handle such interacting random processes on networks, we develop appropriate tools such as lemmas on biased random walks.Comment: Published at http://dx.doi.org/10.1214/14-AAP1023 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Optimal admission policies for small star networks

In this thesis admission stationary policies for small Symmetric Star telecommunication networks in which there are two types of calls requesting access are considered. Arrivals form independent Poisson streams on each route. We consider the routing to be fixed. The holding times of the calls are exponentially distributed periods of time. Rewards are earned for carrying calls and future returns are discounted at a fixed rate. The operation of the network is viewed as a Markov Decision Process and we solve the optimality equation for this network model numerically for a range of small examples by using the policy improvement algorithm of Dynamic Programming. The optimal policies we study involve acceptance or rejection of traffic requests in order to maximise the Total Expected Discounted Reward. Our Star networks are in some respect the simplest networks more complex than single links in isolation but even so only very small examples can be treated numerically. From those examples we find evidence that suggests that despite their complexity, optimal policies have some interesting properties. Admission Price policies are also investigated in this thesis. These policies are not optimal but they are believed to be asymptotically optimal for large networks. In this thesis we investigate if such policies are any good for small networks; we suggest that they are. A reduced state-space model is also considered in which a call on a 2-link route, once accepted, is split into two independent calls on the links involved. This greatly reduces the size of the state-space. We present properties of the optimal policies and the Admission Price policies and conclude that they are very good for the examples considered. Finally we look at Asymmetric Star networks with different number of circuits per link and different exponential holding times. Properties of the optimal policies as well as Admission Price policies are investigated for such networks

Optimal admission control in tandem and parallel queueing systems with applications to computer networks

Modern computer networks require advanced, efficient algorithms to control several aspects of their operations, including routing data packets, access to secure systems and data, capacity and resource allocation, task scheduling, etc. A particular class of problems that arises frequently in computer networks is that of admission and routing control. Two areas where admission control problems are common are traffic control and authentication procedures. This thesis focuses on developing tools to solve problems in these areas. We begin the thesis with a brief introductory chapter describing the problems we will be addressing. Then, we follow this with a review of the relevant literature on the problems we study and the methodologies we use. Then, we have the main body of the dissertation, which is divided into three parts, described below. In the first part, we analyze a problem related to data routing in a network. Specifically, we study the problem of admission control to a system of two stations in tandem with finite buffers, Poisson arrivals to the first station, and exponentially distributed service times at both stations. We assume costs are incurred either when a customer is rejected at the time of arrival to the first station or when the second station is full at the time of service completion at the first station. We propose a Markov decision process formulation for this problem. Then, we use this model to show that, when one of the buffers has size one, the structure of the optimal policy is threshold and that only two particular policies can be optimal. We provide the exact optimality thresholds for small systems. For larger systems, we formulate heuristic policies and use numerical experiments to show that these policies achieve near-optimal performance. For the second part of this thesis, we investigate the system described above in a more general case, where the capacity of the buffers at both station is equal, finite and arbitrary. We focus on two specific, extremal policies, which we call the Prudent and Greedy policies. We derive a closed-form expression for the long-run average reward under the Prudent policy and provide a necessary and sufficient threshold condition for it to be optimal. For the Greedy policy, we give a matrix-analytic solution for the long-run average reward and provide a sufficient condition for it to be optimal. We also prove that it is always optimal to admit customers in the states where the Prudent policy admits customers. Next, we use an example to illustrate that the optimal policy can have a complicated form. Finally, we propose two heuristic policies and use numerical experiments to show that they perform much better than the Prudent and Greedy policies, and in fact, achieve near-optimal performance. In the third and final part of this dissertation, we shift our attention to a different admission and routing control problem. We study a centralized system where requests for authentication arrive from different users. The system has multiple authentication methods available and a controller must decide how to assign a method to each request. We consider three different performance measures: usability, operating cost, and security. First, we model the problem using a cost-based approach, which assigns a cost to each measure of performance. Under this approach, we find that if each authentication method has infinitely many servers the optimal policy is static and deterministic. On the other hand, if there is one method that has finite capacity and the rest have infinitely many servers, we show that the optimal policy is of trunk reservation form. Then, we model the problem using a constraint-based approach, which assumes hard constraints on some of the measures of performance. We show that if each method has infinitely many servers, the optimal policy is static and randomized. While, if one method has finite capacity and the rest have infinitely many servers, we show that the optimal policy has a 2-randomized trunk reservation form. Finally, we illustrate how to use our results to construct an efficient frontier of non-dominated solutions. We end this dissertation with a short recapitulation of our main contributions and a discussion on potential avenues for future research.Ph.D