A theoretical model of an n-dimensional toroidal interconnection network with virtual cut-through routing is developed. Network performance is analyzed as a function of message load for various network and communication parameters. An exact analytical expression for the network’s saturation point is derived, alongside latency as a function of message generation rate using a mean-field theory approximation. The analysis is based on a Markov chain description of the routing queueing system. This innovative analysis solidifies the relationship and explains the saturation point being proportional to the number of torus dimensions and inversely proportional to the length of the path from the source to the destination and the message length (i.e. link processing time). It was found that the transition from steady state to saturation is a second-order (continuous) phase transition with a critical exponent equal to 1. Simulation results show very good agreement with the theoretical analysis.

An analytical model of a network with 2-dim torus topology and virtual cut-through routing has been considered in order to find out and analyze certain relationships between network parameters, load and performance. An exact expression for the saturation point (message generation rate at which network saturates) and expressions for the latency as a function of the message generation rate under the assumptions of the mean field theory have been obtained. It has been found that the saturation point is inversely proportional to the message length and to the distance between the source and destination. The theoretical results are in a good agreement with small-scale simulation experiments.

A simple network model with torus topology and the virtual cut-through routing has been considered in order to find out and analyze certain relationships between network parameters, load and performance. Simulation experiments for various values of network parameters (mesh size, message path length, and message length) have been performed. It is found that if the mesh linear dimension is at least twice as large as the message path length (the distance from source to destination) the network behavior (latency and saturation point) does not depend on the mesh size. Both theoretical and empirical results show that the saturation point is inversely proportional to the message length. If the network is in the steady state, a good agreement with Little’s theorem has been observed.

Theoretical models and numerical results for performance of the computer interconnection networks with heterogeneous activity are presented. The networks are modeled as a ring or as 2-dim toroidal square lattice of nodes with local processors with two or, respectively, four output ports/buffers. The processors generate messages with two different rates, λ 1 or λ 2 , per clock cycle and per output buffer, depending on the intensity of the flow of the arriving messages. The average queue lengths and average latencies are obtained. The model of independent queues and the Jackson theorem are not applicable for this type of networks. It is shown that the networks undergo the phase transition of the second order with non-trivial critical exponents.

A simple network model with torus topology and the virtual cut-through routing have been considered in order to find out and analyze certain relationships that can be used as a starting point for a deeper theoretical analysis and further research. An expression for the saturation point (message generation rate at which network saturates) and approximate expressions for the latency as a function of the message generation rate have been obtained. Simulation experiments for various values of network parameters (mesh size, message path length, and message length) have been performed. It is found that if the mesh linear dimension is at least twice as large as the message path length (the distance from source to destination) the network behavior (latency and saturation point) does not depend on the mesh size. Both theoretical and empirical results show that the saturation point is inversely proportional to the message length.

This paper presents theoretical and numerical results for the performance of a multiprocessor network modeled as a ring and as a toroidal square lattice of nodes with local processors that generate messages for output ports/buffers. The output buffers are assumed to have infinite capacity and service time is deterministic. Two models are considered. One assumes that every processor generates messages with rate λ per time slot and per output port/buffer. The other model considers that the generation rate of a node depends on the intensity of the flow of arriving messages. Explicit expressions for the distribution of queue lengths, the average number of messages in the buffers, the average latency and the critical network load depending on distance between the source and the destination are obtained. Simulation results show excellent agreement with theoretical predictions based on the assumption of independent queues.

A most common way to store information is to encode it in the optical properties of an object and to retrieve it by viewing the object by reflected and transmitted natural (thermalized) light-or even by light emitted by the object itself-for a specified time interval. The discreteness of the radiation degrees of freedom and the statistical properties of thermal (incoherent) radiation impose limitations on the amount of the retrieved information.We derive the maximum information that can be retrieved from the object. This amount is always finite and is proportional to the area of the object, the solid angle under which the entrance pupil of the receiver is seen from the object, and the time of observation. An explicit expression for the information in the case where the information recorded by the receiver obeys Planck's spectral distribution is obtained. The amount of information per photon of recorded radiation is a universal numerical constant, independent of the parameters of observation.

This index covers all technical items - papers, correspondence, reviews, etc. - that appeared in this periodical during the year, and items from previous years that were commented upon or corrected in this year. Departments and other items may also be covered if they have been judged to have archival value. The Author Index contains the primary entry for each item, listed under the first author's name. The primary entry includes the co-authors' names, the title of the paper or other item, and its location, specified by the publication abbreviation, year, month, and inclusive pagination. The Subject Index contains entries describing the item under all appropriate subject headings, plus the first author's name, the publication abbreviation, month, and year, and inclusive pages. Note that the item title is found only under he primary entry in the Author Index.

We consider the physical limitations imposed on the information content of an image by the wave and quantum nature of light, when the image is obtained by illuminating a reflecting or transmitting planar object by natural---i.e., fully thermalized---light, or by observation of an object emitting incoherent (thermal) radiation. The discreteness of the degrees of freedom and the statistical properties of thermal radiation are taken into account. We derive the maximum amount of information that can be retrieved from the object. This amount is always finite and is proportional to the area of the object, the solid angle under which the entrance pupil of the receiver is seen from the object, and the time of observation. An explicit expression for the information in the case where the information recorded by the receiver obeys Planck's spectral distribution is obtained. The amount of information per photon of recorded radiation is a universal numerical constant, independent of the parameters of observation.

We consider the physical limitations imposed on the information content of an image by the wave and quantum nature of light, when the image is obtained by illuminating a reflecting or transmitting planar object by natural (i.e., fully thermalized) light, or by observation of an object emitting incoherent (thermal) radiation. The discreteness of the degrees of freedom and the statistical properties of thermal radiation are taken into account. We derive the maximum amount of information that can be retrieved from the object. This amount is always finite and is proportional to the area of the object, the solid angle under which the entrance pupil of the receiver is seen from the object, and the time of observation. An explicit expression for the information in the case where the information recorded by the receiver obeys Planck’s spectral distribution is obtained. The amount of information per photon of recorded radiation is a universal numerical constant, independent of the parameters of observation.

In this paper, we consider the problem of constructing minimal cycle-breaking connectivity preserving sets of turns for graphs that model communication networks, as a method to prevent deadlocks. Cycle-breaking provides for deadlock-free wormhole routing constrained by turns prohibited at some nodes. We present lower and upper bounds for minimal cardinalities of cycle-breaking connectivity preserving sets for several classes of graphs such as homogeneous meshes, \mbi p-ary \mbi n-cubes, cube-connected cycles, hexagonal and honeycomb meshes, tori, etc.

In this chapter, the problem of constructing minimal cycle-breaking connectivity preserving sets of turns for graphs that model regular or near regular multiprocessor systems, as a method to prevent deadlocks is investigated. Cycle-breaking provides for deadlock-free wormhole routing defined by turns prohibited at some nodes. The lower and upper bounds for minimal cardinalities of cycle-breaking connectivity preserving sets for several classes of graphs such as homogeneous meshes, p-ary n-cubes, cube-connected cycles, hexagonal and honeycomb meshes and tori, Hamiltonian graphs and others are obtained and presented along with some preliminary experimental results.

It is shown how information contained in the pair-wise correlations between atoms of a gas can be used to convert completely heat taken from a thermostat into mechanical work in a process of relaxation of the system to its thermal equilibrium state. Both classical correlations and quantum correlations (entanglement) are considered. The amount of heat converted into work is proportional to the entropy defect of the initial state of the system. The equivalence relation between information and work is explicitly demonstrated for the case of two-particle correlations. The amount of work obtained per particle is twice as large in the case of entanglement as in the case of classical correlations.

This paper is devoted to networks with different size of buffers (5, 10, 20, 30, 40, and 50). The ring and the two-dimension torus topology networks are considered, and the results are compared with these for networks with infinite buffers. The network behavior in terms of the average number of messages and the latency has been studied. Both second-order and first-order transitions to the saturation state have been observed. The results show that the model of independent queues, which is valid for networks with infinite buffers, is still applicable for the load values outside of the critical region, but breaks down, which violates the Jackson theorem.

It is shown how information contained in the pairwise correlations (in general, partial) between atoms of a gas can be used to completely convert heat taken from a thermostat into mechanical work in a process of relaxation of the system to its thermal equilibrium state. Both classical correlations and quantum correlations (entanglement) are considered. The amount of heat converted into work is proportional to the entropy defect of the initial state of the system. For fully correlated particles, in the case of entanglement the amount of work obtained per particle is twice as large as in the case of classical correlations. However, in the case of entanglement, the amount of work does not depend on the degree of correlation, in contrast to the case of classical correlations. The results explicitly demonstrate the equivalence relation between information and work for the case of two-particle correlations.

The problem of preventing deadlocks and livelocks in computer communication networks with wormhole routing is considered. The method to prevent deadlocks is to prohibit certain turns (i.e., the use of certain pairs of connected edges) in the routing process, in such a way that eliminates all cycles in the graph. A new algorithm that constructs a minimal (irreducible) set of turns that breaks all cycles and preserves connectivity of the graph is proposed and analyzed. The algorithm is tree-free and is considerably simpler than earlier cycle-breaking algorithms. The properties of the algorithm are proven and lower and upper bounds for minimum cardinalities of cycle-breaking connectivity preserving sets for graphs of general topology as well as for planar graphs are presented. In particular, the algorithm guarantees that not more than 1/3 of all turns in the network become prohibited. Experimental results are presented on the fraction of prohibited turns, the distance dilation, as well as on the message delivery times and saturation loads for the proposed algorithm in comparison with known tree-based algorithms. The proposed algorithm outperforms the treebased algorithms in all characteristics that were considered. DEADLOCK PREVENTION IN NETWORK OF WORKSTATIONS 3 Deadlock Prevention in Network of Workstations with Wormhole Routing

We present theoretical and numerical results for the performance of a multiprocessor network modeled as a ring and as a toroidal square lattice of nodes with local processors that generate messages for output ports/buffers. The output buffers are assumed to have infinite capacity, and the service time is deterministic. Two models are considered. One assumes that every processor generates messages with rate λ per time slot and per output port/buffer. The other model considers that the generation rate of a node depends on the intensity of the flow of arriving messages. Explicit expressions for the distribution of queue lengths, the average number of messages in the buffers, the average latency, and the critical network load depending on the distance between the source and the destination are obtained. Simulation results show excellent agreement with theoretical predictions based on the assumption of independent queues.

The problem of preventing deadlocks and livelocks in computer communication networks, in particular, those with wormhole routing, is considered. The method to prevent deadlocks is to prohibit certain turns (i.e., the use of certain pairs of connected edges) in the routing process, in such a way that eliminates all cycles in the graph. We propose a new algorithm that constructs a minimal (irreducible) set of turns that breaks all cycles and preserves connectivity of the graph. The algorithm is tree-free and is considerably simpler than earlier cycle-breaking algorithms. We prove its properties and present lower and upper bounds for minimum cardinalities of cycle-breaking connectivity preserving sets for graphs of general topology as well as for planar graphs. In particular, the algorithm guarantees that not more than 1/3 of all turns in the network become prohibited. We also present experimental results on the fraction of prohibited turns, the distance dilation, as well as on the message delivery times and saturation loads for the proposed algorithm in comparison with known tree-based algorithms. The proposed algorithm outperforms substantially the tree-based algorithms in all characteristics considered.