Dynamic Routing Problem Research Articles

On computing Markov decision theory-based cost for routing in circuit-switched broadband networks

In this paper, we study the problem of dynamic routing in multi-service circuitswitched networks. In a previous work, we have proposed a distributed, state dependent, dynamic routing method, called Least Cost Routing in Multi-Service Networks (LCRM), for multirate circuit-switched networks. Broadband Integrated Services Digital Networks (BISDN) should be capable of supporting a variety of traffic classes (e. g. data, voice, video, facsimile), each of which has its own traffic requirement (bandwidth requirement, call arrival rate, and call holding time) and reward parameter. The LCRM method is obtained through the policy iteration routine of Markov decision theory. It represents a one-step policy improvement on a base policy π0, with direct link routing only. The policy π0 also requires that each call class has a portion of link bandwidth dedicated to it. In this paper, we look for an efficient computational way to obtain the corresponding relative cost values, which represent the cost of routing a call over one link. We consider the one-linke model with two types of traffic. We show that the system of linear equations associated with the two-dimensional Markov chain can be decomposed into a system of linear equation associated with the one-dimensional Markov chain. Examples with two classes of service are presented.

Dynamic routing and admission control for virtual circuit networks

The dynamic joint routing and admission control problem in multiple class multiple source-destination virtual circuit networks is considered. A nonlinear dynamic queueing model for virtual circuit networks that considers the dynamic interaction among the virtual circuit and packet processes is introduced. Then a multi-objective cost function of rejecting and maintaining virtual circuits, as well as of delaying and servicing packets is defined. The combined problem is formulated as an optimal control problem. Necessary optimality conditions are provided by Pontryagin's maximum principle. Sufficient optimality conditions based on the convexity of the Hamiltonian function are also given. For the finite horizon, the optimal controls can be found after numerically solving a Two-Point Boundary-Value Problem. For the longrun stationary equilibrium, the state-dependent routing and admission controls are derived.

Analysis of networks of queues via projection techniques

In this research, the author deviates from the conventional traffic models and approaches. The author uses a traffic model proposed by Cruz (1990). In Cruz's model, the rate functions of traffic sources are assumed to satisfy some linear "burstiness constraints". Such traffic models can be used to describe a class of rate-based flow-controlled sources. A state vector is defined to describe the queueing system. The author divides the operation of the studied queueing system into multiple phases. For each phase, the author writes a system equation to describe completely the behavior of this studied queueing system. The author then proposes the iterative feasible set method to identify the feasible region of the state vector using some linear programming techniques and other existing theorems regarding the projection of convex sets into a space with a lower dimension. Using the above technique, the author studied the performance of three routing schemes in a simple dynamic routing problem, namely the route to shortest rule, the fixed routing rule and the bounded linear rule. The author first identified the feasible regions of a defined state vector for each routing scheme using the proposed method. From the identified feasible regions, the author then analyzed the extremal performance of these routing schemes and compared their performances.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An algorithm for dynamic routing in FMS under an unpredicted failure

The problem of dynamic part routing in an automated manufacturing system is described. The system consists of workstations capable of performing a number of different operations on a family of parts. In view of the unreliability of machines the production control system should manage the production schedule, given the random pattern of machine failure/repair. A three-level hierarchial control structure is suggested and simulated, using stochastic generation of events and part movements. The obtained results show that a production profile derived under the developed controller is feasible.

A computationally efficient iterative solution of the multidestination optimal dynamic routing problem

The dynamic routing problem for multiple destination networks is considered. The minimum time rather than total delay cost functional is employed. The problem is solved through an iterative link-by-link optimization. Each link capacity is optimally partitioned by examining the upper bounds for the evacuation time imposed through different capacity allocations for each origin/destination pair traffic. The computational complexity per iteration is polynomial in the number of network nodes. This is due to the examination of origin/destination pairs rather then destinations alone as in previous work where a similar approach led to exponential complexity. Sufficient conditions for the convergence of the iterative algorithm to the optimum are given. If these are not satisfied supplementary steps are described which conduct the algorithm to the desired solution. These involve exponential computational complexity.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Optimal dynamic routing in double ring networks

The dynamic routing problem with multiple destinations on ring networks is examined. The authors discuss the peculiarities of the ring topology as well as the resulting simplification for the dynamic routing problem. The problem is transformed into a problem that minimizes link evacuation times. It involves a minimax cost and is equivalent to a linear program admitting a finite solution. A different approach is then taken: a solution based on an infinite algorithm is proposed and used to obtain a complexity of only O( mod N mod /sup 3/) per iteration and an exponential rate of convergence to the minimal value. Several optimal routing policies are characterized and formulated. It is found that the store-and-forward feature is not necessary in order to implement a particular optimal routing. Optimality can be achieved by a relatively simple protocol reminiscent of accessing procedures in local area networks. The incorporation of external arrival rates is discussed. Examples are worked out, and suggestions for future work are given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Martingale dynamics and optimal routing in a network

In this paper, we consider a dynamic routing problem in a store-and-forward computer-communication network which consists of l parallel channels connected between the source and the destination. We prove that if messages arrive at the network in accordance with a Poisson process and all nodes have an exponential service rate, then the routing strategy that minimizes the total expected time in transmitting all messages that arrive before T>0 is to route the arriving message to the channel along which the sum of all queue sizes is minimum. Techniques of martingale and dynamic programming are used in obtaining the result.

Minimum‐delay routing in continuous‐time dynamic networks with Piecewise‐constant capacities

AbstractA single‐source single‐sink dynamic network is considered where the link flows are real‐valued measurable functions defined on a time interval and where storage is allowed at the nodes. Piecewise‐constant link and storage capacities are given. A τ‐maximum flow is a dynamic flow assignment that maximizes the total amount of commodity reaching the sink before time τ. The problem considered is that of computing a flow which is simultaneously τ‐maximum for all τ. Such a flow solves a minimum‐delay dynamic routing problem. An algorithm is presented which computes an optimal flow in O( | N | 4T4) time, where | N | is the number of nodes and T is the number of times that the capacities change. Previous polynomial‐time algorithms have been given only for the case of constant capacities.

Optimal Dynamic Routing in Multidestination Networks

The dynamic routing problem for multiple destination networks is considered. The minimum time rather than total delay cost functional is employed. Each link capacity is optimally partitioned by examining the competition of bottlenecks associated with each destination. The multidestination problem is thus solved through an iterative link-by-link optimization.

Development of optimal routing policies in a queueing network

An approach to the solution of the dynamic routing problem in a queueing network is presented in the paper, based on Lagrangian duality and decomposition techniques. A numerical solution can be obtained by a multilevel off-line computational procedure. The considered network has deterministic inputs and initial state, and the optimization problem is in discrete time. Link capacity and queue length constraints are taken into account.

Convexity and characterization of optimal policies in a dynamic routing problem

An infinite horizon, expected average cost, dynamic routing problem is formulated for a simple failure-prone queueing system, modelled as a continuous time, continuous state controlled stochastic process. We prove that the optimal average cost is independent of the initial state and that the cost-to-go functions of dynamic programming are convex. These results, together with a set of optimality conditions, lead to the conclusion that optimal policies are switching policies, characterized by a set of switching curves (or regions), each curve corresponding to a particular state of the nodes (servers).

An optimal control approach to dynamic routing in networks

This paper explores the application of optimal control theory to the problem of dynamic routing in networks. The approach derives from a continuous state space model for dynamic routing and an associated linear optimal control problem with linear state and control variable inequality constraints. The conceptual form of an algorithm is presented for finding a feedback solution to the optimal control problem when the inputs are assumed to be constant in time. The algorithm employs a combination of necessary conditions, dynamic programming, and linear programming to construct a set of convex polyhedral cones which cover the admissible state space with optimal controls. An implementable form of the algorithm, along with a simple example, is presented for a special class of single destination networks.

A simple dynamic routing problem

As jobs arrive they have to be routed to one of two similar exponential servers. It is shown that if the queue lengths at both servers are observed then the Optimal decision is to route jobs to the shorter queue, whereas if the queue lenths are not observed then it is best to alternate between queues, provided the initial distribution of the two queue sizes is the same. The optimality of these routing strategies is independent of the statistics of the job arrivals.

Minimum cost routing for static network models

AbstractThis paper develops techniques which can be applied to long range planning studies for the domestic long haul communications network. The problem studied is how to select a path through the network for each point‐to‐point demand for communications channels, so that the total network cost is minimized. The problem is to minimize total network cost, subject to multicommodity flow requirements and concave link cost functions. Finding an exact solution is difficult because of the concavity of the cost functions and the complexity (100 to 200 nodes and 200 to 300 links) of the network structure. A specialized technique is developed to provide locally optimal solutions to the problem, one of minimizing a concave function over a convex constraint set. When the link cost displays a fixed charge, a modification of the iterative algorithm provides acceptable a modification of the iterative algorithm provides acceptable solutions. Even though the global optimum cannot be found amidst the immense number of local optima, several sample problems demonstrate the value of the techniques developed.A companion paper will extend this work to the dynamic routing problem, of deciding how to route future demands and install transmission facilities so as to minimize the present worth of expenditures during the study interval. The methods and goals of these modeling efforts will be discussed in the companion paper.