The scheduling of real-time tasks with fault-tolerant requirements has been an important problem in multiprocessor systems. The primary-backup (PB) approach is often used as a fault-tolerant technique to guarantee the deadlines of tasks despite the presence of faults. In this paper we propose a dynamic PB-based task scheduling approach, wherein an allocation parameter is used to search the available time slots for a newly arriving task, and the previously scheduled tasks can be re-scheduled when there is no available time slot for the newly arriving task. In order to improve the schedulability we also propose an overloading strategy for PB-overloading and Backup-backup (BB) overloading. Our proposed task scheduling algorithm is compared with some existing scheduling algorithms in the literature through simulation studies. The results have shown that the task rejection ratio of our real-time task scheduling algorithm is almost 50% lower than the compared algorithms.

Vertically stacked optical banyan (VSOB) is an attractive architecture for constructing banyan-based optical switches. Blocking behaviors analysis is an effective approach to studying network performance and finding a graceful compromise among hardware costs, blocking probability and crosstalk tolerance; however, little has been done on analyzing the blocking behavior of VSOB networks under crosstalk constraint which adds a new dimension to the switching performance. In this paper, we study the overall blocking behavior of a VSOB network under various degree of crosstalk, where an upper bound on the blocking probability of the network is developed. The upper bound depicts accurately the overall blocking behavior of a VSOB network as verified by extensive simulation results and it agrees with the strictly nonblocking condition of the network. The derived upper bound is significant because it reveals the inherent relationship between blocking probability and network hardware cost, by which a desirable tradeoff can be made between them under various degree of crosstalk constraint. Also, the upper bound shows how crosstalk adds a new dimension to the theory of switching systems.

A Superconcentrator is a directed acyclic graph with specific properties. The existence of linear-sized supercentrator has been proved in [4]. Since then, the size has been decreased significantly. The best known size is 28N which is proved by U. Schöning in [8]. Our work follows their construction and proves a smaller size superconcentrator.

A combination of horizontal expansion and vertical stacking of optical Banyan (HVOB) is the general architecture for building Banyan-based optical cross-connects (OXCs), and the intrinsic crosstalk problem of optical signals is a major constraint in designing OXCs. In this paper, we analyze the blocking behavior of HVOB networks and develop the lower bound on blocking probability of a HVOB network that is free of first-order crosstalk in switching elements. The proposed lower-bound is significant because it provides network designers an effective tool to estimate the minimum blocking probability they can expect from a HVOB architecture regardless what kind of routing strategy to be adopted. Our lower bound can accurately depict the overall blocking behavior in terms of the minimum blocking probability in a HVOB network, as verified by extensive simulation based on a network simulator with both random routing and packing routing strategies. Surprisingly, the simulated and theoretical results show that our lower bound can be used to efficiently estimate the blocking probability of HVOB networks applying packing strategy. Thus, our analytical model can guide network designers to find the tradeoff among the number of planes (stacked copies), the number of SEs, the number of stages and blocking probability in a HVOB network applying packing strategy.