Alexander Shulman

Multicommodity Flows in Ring Networks

In this paper, we consider the problem of multicommodity flows in a ring network. Using necessary and sufficient conditions to ensure feasible linear and integral flows in the network, and the special structure of the ring topology, we construct efficient algorithms to route all the demands.

Optimal routing in circuit switched communication networks

We consider the optimal circuit routing problem. The problem consists of accommodating a given circuit demand in an existing circuit-switched network. The objective is to find a circuit accommodation providing the maximum residual capacity over the network under the total circuit cost constraints. Practical considerations require a solution which is robust to the variations in circuit demand and cost. The objective function for the circuit routing problem is not a smooth one. In order to overcome the difficulties of nonsmooth optimization, a sequence of smooth convex optimization problems is considered. The optimal algorithm for the circuit routing problem is obtained as a limiting case of the sequence of the optimal routing strategies for the corresponding smooth optimization problems. The proof of its convergence to the optimal solution is given. This optimization algorithm is capable of efficiently handling networks with a large number of commodities. It also satisfies the above-mentioned robustness requirements. Numerical results are discussed.

Dynamic bandwidth-allocation and path-restoration in SONET self-healing networks

This paper presents a new scheme for real-time bandwidth allocation and path restoration (BARS) in mesh networks via SONET wideband digital cross-connect systems (WDCSs) in response to demand and load dynamics and link and/or node failure(s). The scheme dynamically maximizes bandwidth allocation while ensuring full service restorability. Since the physical network capacity is limited, sometime not all the demand can be accommodated under the full restorability requirement. This demand in SONET BARS is rejected fairly at the network boundary even if capacity for allocation is available. Bandwidth allocation and fair demand admission are optimized jointly under the full restorability requirements. The implementation of SONET WDCS does not need excessive storage. An efficient parallel algorithm for solving the optimization problem is also presented. The algorithm produces superior spare capacity assignments compared to the results in the literature.

Optimal dynamic virtual path bandwidth allocation and restoration in ATM networks

This paper presents an optimal dynamic virtual path (VP) bandwidth allocation and restoration scheme for mesh ATM networks (in the context of the layered traffic control architecture). The scheme integrates the dynamics of demand admission, VP bandwidth allocation, and logical spare capacity assignment for maximizing network throughput while ensuring full traffic restorability. We present an optimal parallel algorithm that minimizes the total rejected bandwidth demand and cell loss while satisfying the maximal cell loss, delay, and 100% restorability requirements for a given set of failure scenarios. The optimal spare capacity assignment in the presented approach follows directly from the network admission and bandwidth allocation decisions. The algorithm also equalizes cell losses on the VPs thus providing cell-level fairness.

A decomposition algorithm for capacity expansion of local access networks

The authors study how to expand capacity of the local access network to meet projected demand over a given planning horizon at minimum cost. The alternatives for capacity expansion include both copper cable and digital multiplexer. They show how the problem can be modeled as an integer programming problem; however, the size of the problem for a typical network and the discontinuous cost structure of the expansion facilities preclude the use of a general purpose integer programming code to solve it. A decomposition approach that takes advantage of the structure of the problem and allows the problem to be solved in a reasonable amount of time is proposed. The solution methods described have been implemented and computational results are discussed. The algorithm forms a part of the network planning system NETCAP that has been in use since 1989. >

An algorithm for capacity expansion of local access networks

An investigation to determine the minimum cost capacity expansion plan for the outside plant network to meet projected demand over a given planning horizon is presented. It is shown how the problem can be modeled as an integer programming problems; however, the size of the problem for a typical network precludes the use of a general-purpose integer programming code. A decomposition approach that takes advantage of the structure of the problem and allows the problem to be solved in a reasonable amount of time is proposed. The solution methods have been implemented and computational results are presented.<<ETX>>

A new algorithm for the solution of the minimum cost multicommodity flow problem

The multicommodity minimum cost flow problem (MMCF) is to determine a minimum cost multicommodity flow through the constrained network. This paper considers a new barrier-penalty optimization algorithm for the solution of a general linear MMCF problem. The algorithm does not require an initial point to be feasible. This algorithm is computationally efficient and allows one to solve MMCF problems with a large number of commodities. It is also applicable to the convex MMCF problems with nonlinear constraints and/or objective function. The proof of its convergence and a new algorithm for calculating a lower bound are presented. The computer implementation of the algorithm is discussed, and computational experience is reported.

Architecture for restorable call allocation and fast VP restoration in mesh ATM networks

This paper presents an architecture for restorable call allocation and fast virtual path (VP) restoration in mesh ATM networks. In this architecture, virtual working and spare capacities needed for call allocation and restoration are reserved and released dynamically on a call-by-call basis at the time of call admission and termination. The architecture does not require advance assignment of spare and working capacities. To shorten the call processing delay, this is done in a parallel-distributed fashion. To provide restorable call allocation, parallel-distributed call processing algorithms of the sender-chooser type are suggested. The algorithms integrate on the call level virtual bandwidth allocation, virtual spare capacity assignment with fixed, alternate, or state-dependent routing. Each routing scheme leads to a particular tradeoff between call processing complexity, call setup delay, and bandwidth efficiency. For each pair of nodes, two sets of VPs are provisioned. The first is a working VP (WVP) set, to be used for call allocation during the normal operation. The second is a spare VP (SVP) set, to be used for VP restoration in the event of failure of network elements (NE). Each SVP protects a preassigned subset of the node pair WVPs. Each SVP is selected to be link/node disjoint from the WVPs that it is assigned to protect. This assures protection of the WVP set by a small number of SVPs. Since SVPs are preset and appropriate virtual spare capacities are reserved in advance, the architecture guarantees full restorability and provides very fast restoration. The restoration is done on the VP level in a self-healing manner. The suggested architecture requires only local information to be maintained at each node.

Burst level congestion control in ATM networks

We present the architecture for burst level congestion control (BLCC) in ATM networks which is well suited for bursty self-similar traffic. The architecture is based upon pre-planned virtual path (PVP) set and preassigned maximal permitted route rates (MPR). The PVP set and MPR are engineered to meet QoS requirements of multi-service demand. The suggested burst level control maintains the maximal rate of cell admission on any PVP below its MPR. This is done at each PVPs source node by regulating bursts admission and by reserving the burst peak rate for each admitted burst. The reservation can be performed very fast since it is done at PVPs source node without any communication with other nodes. The MPR and PVP set are adjusted in a relatively slow, for instance hourly, timeframe adapting to the changes in the demand. The paper also presents an efficient technique for multiclass QoS engineering of burst admission that can be applied to engineer networks with large number of nodes and service classes.

Optimal routing in circuit-switched communication networks

We consider the optimal circuit routing problem. The problem consists of accommodating a given circuit demand in an existing circuit-switched network. The objective is to find a circuit accommodation providing the maximum residual capacity over the network under the total circuit cost constraints. Practical considerations require a solution which is robust to the variations in circuit demand and cost. The objective function for the circuit routing problem is not a smooth one. In order to overcome the difficulties of nonsmooth optimization, a sequence of smooth convex optimization problems is considered. The optimal algorithm for the circuit routing problem is obtained as a limiting case of the sequence of the optimal routing strategies for the corresponding smooth optimization problems. The proof of its convergence to the optimal solution is given. This optimization algorithm is capable of efficiently handling networks with a large number of commodities. It also satisfies the above-mentioned robustness requirements. Numerical results are discussed.