On the Fault-Tolerant Capability of Optimal Constructions of Optical Priority Queues

Construction of optical buffers for packet conflict resolution is one of the most important and challenging issues in all-optical packet switching. Priority queues (PQs) is one of the most general and versatile buffering schemes, and includes the most commonly used first-in first-out (FIFO) queues and last-in first-out (LIFO) queues as special cases. The best constructions of optical PQs currently available was obtained by Cheng et al. by using a feedback architecture consisting of an optical crossbar switch and k groups of optical FIFO multiplexers with delay one (FM1’s), where the i^th group has mi parallel optical ni - to-1 FM1’s (niFM1’s) with the same buffer size Bi (Bi ≥ 1) for i = 1,2,…,k (see Figure 2 in Section I). In this paper, we consider an important practical issue in the constructions of optical PQs: the fault-tolerant capability. We consider the scenario that each group of FM1’s has the same number of FM1’s, say, mi = m for 1 ≤ i ≤ k, and show that the optimal constructions obtained by Cheng et al. possess fault-tolerant capability: the feedback architecture can still be operated as an optical PQ but with a smaller buffer size after up to f FM1’s fail to function properly, where the fault-tolerant capability f can be expressed in terms of the number m of FM1’s in each group and the numbers n1,n2,…,nk of arrival links of the FM1’s in the k groups as f = min1≤i≤k⌊(m − 1)/(ni − 1)⌋. Such a result can be used in the design of the parameters m and n1,n2,…,nk to provide quality of service (QoS) that guarantees a certain level of fault-tolerant capability.