Weconsider a service provider (SP) who provides access to a communication network or some other form of on-line services. Users access the network and initiate calls that belong to a set of diverse service classes, differing in resource requirements, demand pattern, and call duration.

High-speed packet networks will begin to support services that need Quality-of-Service (QoS) guarantees. Guaranteeing QoS typically translates to reserving resources for the duration of a call. We propose a statedependent routing scheme that builds on any base stateindependent routing scheme, by routing flows which are blocked on their primary paths (as selected by the state-independent scheme) onto alternate paths in a manner that is guaranteed---under certain Poisson assumptions---to improve on the performance of the base state-independent scheme. Our scheme only requires each node to have state information of those links that are incident on it. Such a scheme is of value when either the base state-independent scheme is already in place and a complete overhaul of the routing algorithm is undesirable, or when the state (reserved flows) of a link changes fast enough that the timely update of state information is infeasible to all possible call-originators. The performance improvements ...

Modern communication networks are able to respond to randomly uctuating demands and failures by allowing bu ers to ll, by rerouting tra c and by reallocating resources. They are able to do this so well that, in many respects, largescale networks appear as coherent, almost intelligent, organisms. The design and control of such networks present challenges of a mathematical, engineering and economic nature. In this lecture I describe some of the models that have proved useful in the analysis of stability, statistical sharing and pricing, in systems ranging from the telephone networks of today to the information superhighways of tomorrow.

We consider Virtual Partitioning (VP), a scheme for sharing a resource among several traffic classes in an efficient, fair, and robust manner. In the preliminary design stage, each traffic class is allocated a nominal capacity, which is based on expected offered traffic and required quality-of-service. During operations, if the current capacity usage by a class exceeds its nominal allocation, then it is declared to be in `overload', and a state-dependent trunk reservation mechanism gives it lower priority in the admission of new calls. We develop efficient computational algorithms for the case of heterogeneous traffic, and perform extensive numerical experiments to demonstrate the accuracy of the various approximations. The performance of VP is examined and compared to that of Complete Sharing and Complete Partitioning. Particular weight is placed on robustness, meaning that traffic classes with arrival rates conforming to the design continue to receive the required quality-of-service,...

In this paper we consider the analysis of call blocking at a single resource with differing capacity requirements as well as differing arrival rates and holding times. We include in our analysis trunk reservation parameters which provide an important mechanism for tuning the relative call blockings to desired levels. We base our work on an asymptotic regime where the resource is in heavy traffic. We further derive, from our asymptotic analysis, methods for the analysis of finite systems. Empirical results suggest that these methods perform well for a wide class of examples. LOSS NETWORKS; INTEGRATED NETWORKS; TIME-SCALE SEPARATION; TRUNK RESERVATION; BLOCKING PROBABILITIES AMS 1991 Mathematics Subject Classification Primary: 60K20 Secondary: 60K15, 60K30, 68M20, 90B12 1 Introduction Recent developments in communication networks have lead to much interest in systems where traffic of widely differing characteristics is integrated. In this paper we address one of the probabilistic issue...

Abstract-Overloads that occur during times of network stress result in blocked access to all users, independent of importance. These overloads can occur because of degraded resource availability or abnormally high demand. Public broadband networks must dynamically recognize some multimedia connections as having greater importance than others and allocate resources accordingly. A new approach to connection admission control is proposed that uses an upper limit policy to optimize the admission of connections based on the weighted sum of blocking across traffic classes. This results in a simple algorithm suitable for multimedia and packet networks. This work is also the first to demonstrate that the use of an upper limit policy is superior to traditional approaches of adding extra capacity or partitioning capacity, both in terms of the amount of resources required and sensitivity to load variations. An upper limit policy can also be deployed much faster when a large overload occurs from a disaster event. I.

The design of connection admission control (CAC) for a simple Markovian model of a multiservice statistical multiplexer is considered. The paper begins by laying the foundation through several fundamental analytic concepts, such as a Semi-Markov Decision Process formulation of the design problem and time scale decomposition, before progressively leading up to real world requirements, like robustness and simplicity of design. Several numerical illustrations are given. The salient contributions of the paper are : (1) A unified treatment of multiclass cell and call QoS. (2) A CAC design which is robust, i.e., fair and efficient. (3) Simplicity in the CAC design, together with an evaluation of the tradeoff with performance. (4) An analytic technique for computing the feasibility region in the space of call arrival rates where some control exists to satisfy QoS. (5) The discovery of near linearity of the boundary of the feasible region, which is then used to decompose the design problem. (6...

Motivated by the inability of current drug treatment to provide long-term benefit to HIV-infected individuals, we derive HIV therapeutic strategies by formulating and analyzing a mathematical control problem. The model tracks the dynamics of uninfected and infected CD4 + cells and free plasma virus, and allows the virus to mutate into various strains. At each point in time, several different therapeutic options are available, where each option corresponds to a combination of reverse transcriptase inhibitors. The controller observes the individual’s current status and chooses among the therapeutic options in a dynamic fashion in order to minimize the total viral load. Our initial numerical results suggest that dynamic therapies have the potential to significantly outperform the static protocols that are currently in use; by anticipating and responding to the disease progression, the dynamic strategy reduces the total free virus, increases the uninfected CD4 + count, and delays the emergence of drug-resistant strains. � 1997 Academic Press Limited 1.

: Hierarchical Virtual Partitioning facilitates sharing of a resource, such as a link, by multiple customers, each with multiple service classes. Calls of each service class have distinctive bandwidth requirements, arrival rates and mean holding times. The quality of service is in terms of call blocking probabilities. The algorithms allow the desired mix of fairness, robustness and multiplexing efficiency at each of two levels, namely, customers and the various services of each customer. The scheme relies on nominal allocations of capacities to each customer and service, and priorities in the call admission process, which are implemented by dynamic trunk reservations. An approximate method of analysis based on fixed point equations is given. A reward/penalty paradigm is devised to reflect the issues in Virtual Private Networking and the performance of our algorithm compared to the optimal solution. The results show that the scheme is fair, efficient and robust. I. Introduction Hierarc...

. This paper reviews some current work on routing in loss and queueing networks. We describe two classes of bound on the performance of any dynamic routing scheme, together with some open questions concerning whether the bounds can be approached under certain limiting regimes. The first class of bound is particularly appropriate for networks in heavy traffic, where the key feature of a good routing scheme is its effective utilization of various pooled resources identified by a fluid version of the routing problem. The second class of bound is particularly appropriate for highly connected networks, with many alternative paths. Again, a network flow representation is central, but this time involving a collection of Markov decision processes, one for each resource of the network. Despite their simplicity, the bounds are able to identify the great variety of qualitatively distinct behaviour expected of a good dynamic routing scheme, depending on a network's size, connectivity, asymmetry an...