Edge disjoint paths with minimum delay subject to reliability constraint

Abstract

Recently, multipaths solutions have been proposed to improve the quality-of-service (QoS) in communication networks (CN). This paper describes a problem, λDP/RD, to obtain the λ-edge-disjoint-path-set such that its reliability is at least R and its delay is minimal, for λ≥1. λDP/RD is useful for applications that require noncompromised reliability while demanding minimum delay. In this paper we propose an approximate algorithm based on the Lagrange-relaxation to solve the problem. Our solution produces λDP that meets the reliability constraint R with delay (1+k)D min , for k≥1, and D min is the minimum path delay of any λDP in the CN. Simulations on forty randomly generated CNs show that our polynomial time algorithm produced λDP with delay and reliability comparable to those obtained using the exponential time brute-force approach. Keywordsapproximate algorithm; Lagrange relaxation;multi-constrained edge disjoint paths; network reliability; network delay. I. INTRODUCTIONHE disjoint path set solutions [1][2][3][4][5][6] have been proposed to improve the end-to-end quality-of-service (QoS) of the communication networks (CN). Since the number of vertex disjoint paths in general is very limited, the edge disjoint path (DP) set that do not share edges is more commonly used [7]. References [1,6,8] propose algorithms to improve the reliability of CNs using DP.Reference [9] also shows that the lifetime of an end-to-end communication can be improved with a higher reliability DP.Some CNs, such as those for time critical systems and multimedia applications, are subjected to multi-constrained QoS, e.g., reliability, delay, cost and bandwidth. [8] considers cost and delay as the constraint parameters, [10,11] consider cost and reliability and [4] uses reliability and delay. Note that the problem for generating a DP with two or more constraints has been shown NP-hard [12], and therefore heuristic and approximation algorithms [8,13,14] have been proposed to address the problem.Orda and Sprintson [13] proposed four approximation algorithms to find two delay-constrained DPs with minimum total cost (2DP/DC). For a CN that contains two DPs with delay≤D and minimal cost OPT, their best algorithm, 2DP-4, always finds 2DP/DC with delay≤(1+1/k)D and cost≤k(1+ )(1+ )OPT, where k is a positive integer representing the approximate index, is a small value bounded by 2(log k + 1)/k and is an approximate factor. Applying Lagrange-relaxation, Peng and Shen proposed an algorithm (PSA for short) [8] that improves the performance of 2DP-4 to a delay≤(1+1/k)D with cost≤(1+k)OPT. They showed that PSA can be used to obtain λDP/DC, for λ>2. However, both algorithms in [13] and [8] have one significant limitation; they concentrate on finding only 2DP that satisfy the delay and cost constraints whereas other DP may also satisfy the user defined preconditions. In addition, no simulations were performed to benchmark the feasibility of the algorithms and find the optimal value of k. Loh, et al [2] have recently described a problem to obtain λDP/DRthe se...

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