Alexander Birman

Routing and wavelength assignment methods in single-hop all-optical networks with blocking

We consider single-hop all-optical networks in which wavelength-routed connections (lightpaths) between source-destination pairs are dynamically established and torn down in response to a random pattern of arriving connection requests and connection holding times. A connection request may be blocked if no wavelength is available on a suitable path from source to destination. For these networks we consider several methods for routing and wavelength assignment which combine in various ways three main principles: wavelength reservation, protecting threshold and alternate routes. The methods are evaluated and compared in two case studies. In this type of network the traffic over lightpaths consisting of multiple links is susceptible to high blocking probabilities, which can interfere with the quality of service requirements. It is shown that some of the routing and wavelength assignment methods studied have the potential to overcome this difficulty.

An optimal service policy for buffer systems

Consider a switching component in a packet-switching network, where messages from several incoming channels arrive and are routed to appropriate outgoing ports according to a service policy. One requirement in the design of such a system is to determine the buffer storage necessary at the input of each channel and the policy for serving these buffers that will prevent buffer overflow and the corresponding loss of messages. In this paper, a class of buffer service policies, called Least Time to Reach Bound (LTRB), is introduced that guarantees no overflow, and for which the buffer size required at each input channel is independent of the number of channels and their relative speeds. Further, the storage requirement is only twice the maximal length of a message in all cases, and as a consequence the class is shown to be optimal in the sense that any nonoverflowing policy requires at least as much storage as LTRB.

Asymptotic evaluation of closed queueing networks with many stations

Asymptotic formulas are derived for the partition function of multichain closed product form networks with groups of stations, each group consisting of many identical stations. The derivation of the asymptotic expansion is based on an integral representation of the partition function in a multidimensional complex space and its evaluation using the saddle point method. The saddle point method is also used to derive an iterative algorithm which reduces the problem of solving the multichain network to a set of single chain problems. The accuracy of the approximations is evaluated in two case studies: a memory interference model in a multiprocessing system and a model of a multiprogramming system.

Asymptotic analysis of closed queueing networks with bottlenecks

Asymptotic formulas are derived for the partition function of a class of closed product form networks with queue dependent service rates. The paper thus extends a recently developed method for the asymptotic evaluation of the partition function based on its integral representation in complex space and the saddle point method. Asymptotics are derived for the partition function in normal, moderate and heavy traffic conditions at the bottleneck nodes. The accuracy of the approximations is evaluated through numerical case studies.

Parsing algorithms with backtrack

Two classes of restricted top down parsing algorithms using backtrack are considered. We show that the smaller class recognizes all deterministic context free languages, and that both classes can be simulated in linear time on a random access machine. Certain generalizations of these parsing algorithms are shown equivalent to the larger class. Finally, some decision and closure properties of the classes of languages defined are given.

Error bounds for asymptotic approximations of the partition function

We consider Markovian queueing models with a finite number of states and a product form solution for its steady state probability distribution. Starting from the integral representation for the partition function in complex space we construct error bounds for its asymptotic expansion obtained by the saddle point method. The derivation of error bounds is based on an idea by Olver applicable to integral transforms with an exponentially decaying kernel. The bounds are expressed in terms of the supremum of a certain function and are asymptotic to the absolute value of the first neglected term in the expansion as the large parameter approaches infinity. The application of these error bounds is illustrated for two classes of queueing models: loss systems and single chain closed queueing networks.

A high-performance switch with applications to frame relay networks

A design is proposed for an n*n switch to be used in frame relay networks. The design is based on a single storage unit for packets and hardware-based mechanism for handling simultaneously arriving packets over different input channels which may be intended for the same output channel. The switch is flexible in that it can handle variable length packets, a large number of input/output channels, and a wide range of channel speeds. It can perform cut-through switching and thus decrease packet delay through the network. It allows the design of high-throughput frame-relay nodes, simplifying the design and management of large networks. Its use of a hardware-implemented dynamic scheme for allocating storage allows efficient utilization of buffer space.<<ETX>>