Asymptotic results for partial concentrators

Various switching network construction advantageously use modules known as partial concentrators. A partial concentrator is an n-input, m-output, single-stage switching device in which each input has access to some but not all of the outputs. A partial concentrator is said to have capacity c, if, for any k⩽c inputs, there exist k disjoint paths from the k inputs to some set of k outputs. Here, capacity values achievable for large n when each input has access to exactly M outputs, are considered. For a partial concentrator in which each input has access to exactly M outputs, it is shown that the cost ratio can be made arbitrarily small for any fixed M⩾2. In addition, it is shown that the rate of decrease of the cost ratio with increasing n is logarithmic for M=2, and polynomial for M⩾3     

Performance of a packet switch with crossbar architecture

A packet having a crossbar architecture with M inputs and N outputs is considered. Following earlier work, the theoretical capacity of such a switch is found in terms of the throughput of a closed queueing network. A state-dependent server model that approximates the rate at which the switch is transferring packets as a function of the work backlog (the number of packets queued at the switch inputs) is then developed. In this way, the model reflects the fact that such a switch tends to function more efficiently as the work backlog increases. This model yields an accurate method for approximating the entire distribution of the work backlog, as well as mean queue lengths and waiting times     

Queueing in high-performance packet switching

The authors study the performance of four different approaches for providing the queuing necessary to smooth fluctuations in packet arrivals to a high-performance packet switch. They are (1) input queuing, where a separate buffer is provided at each input to the switch; (2) input smoothing, where a frame of b packets is stored at each of the input line to the switch and simultaneously launched into a switch fabric of size Nb×Nb; (3) output queuing, where packets are queued in a separate first-in first-out (FIFO) buffer located at each output of the switch; and (4) completely shared buffering, where all queuing is done at the outputs and all buffers are completely shared among all the output lines. Input queues saturate at an offered load that depends on the service policy and the number of inputs N, but is approximately 0.586 with FIFO buffers when N is large. Output queuing and completely shared buffering both achieve the optimal throughput-delay performance for any packet switch. However, compared to output queuing, completely shared buffering requires less buffer memory at the expense of an increase in switch fabric size     

An approximate performance analysis of interconnected token-passingrings

An analysis of the performance, in terms of average message delay, is presented for a system of interconnected ring networks. The system is hierarchical, with local rings served by a high-speed backbone ring through gateway queues. In both the local and the backbone rings, the access technique employed is token passing. Service disciplines, with and without priority, have been studied. In the former, priority is given to inter-ring traffic over local traffic. The study makes use of certain results on average delay in systems where the customer initiating a busy period receives special service for the M/G/1 queue with nonpreemptive priority and for the G/G/1 queue. The analysis, which involved several approximations, was verified by simulation     

Polling systems with simultaneous arrivals

The authors analyze polling systems with multiple types of simultaneous arrivals, namely, batches of customers may arrive at the different queues at an arrival epoch. The authors consider cyclic polling systems with N queues, general service time distribution in each queue, and general switchover times. For both the exhaustive and the gated service disciplines the authors derive the necessary equations for computing the N expected waiting time figures. A pseudo conservation law for these system is also derived. The authors compare several special cases of the correlated arrivals polling system, discuss the computational aspects of the numerical method, and examine the applicability of the analysis to other polling systems     

Pass-transistor asynchronous sequential circuits

Design methods for asynchronous sequential pass-transistor circuits, which result in circuits that are hazard- and critical-race-free and which have added degrees of freedom for the input signals, are discussed. The design procedures are straightforward and easy to implement. Two single-transition-time state assignment methods are presented, and hardware bounds for each are established. A surprising result is that the hardware realizations for each next state variable and output variable is identical for a given flow table. Thus, a state machine with N states and M outputs can be constructed using a single layout replicated N+M times     

Heterogeneous bursty traffic dispersion over multiple server clusters

This letter presents performance analysis of multiple subnets, each representing a cluster of computing server nodes, that are introduced with non-uniformly distributed bursty packet arrivals. In particular, we study the case of a multi-state Markov-modulated arrival process, heterogeneously dispersed among designated queues. Cluster processing is modeled by employing a batch service discipline. The probability generating functions of the interarrival times distributions are utilized to derive closed-form expressions for each of the queue size distributions.     

Packet error probabilities in frequency-hopped spread-spectrumpacket radio networks-memoryless frequency-hopping patterns considered

The packet error probability induced in a frequency-hopped spread-spectrum packet radio network is computed. The frequency spectrum is divided into q frequency bins. Each packet is exactly one codeword from an (M, L) Reed-Solomon code [M=number of codeword symbols (bytes); L=number of information symbols (bytes)]. Every user in the network sends each of the M bytes of his packet at a frequency chosen among the q frequencies with equal probability and independently of the frequencies chosen for other bytes (i.e., memoryless frequency-hopping patterns). Statistically independent frequency-hopping patterns correspond to different users in the network. Provided that K users have simultaneously transmitted their packets on the channel and a receiver has locked on to one of these K packets, the probability that this packet is not decoded correctly is evaluated. It is also shown that although memoryless frequency-hopping patterns are utilized, the byte errors at the receiver are not statistically independent; instead they exhibit a Markovian structure     

Modeling and dynamic scheduling of a queueing system with blockingand starvation

Consideration is given to the problem of dynamically controlling a computer communication network consisting of N stations that compete for the use of a single channel. The channel is needed by the stations in order to transfer the packetized information they got from independent sources to a central storage device. The stations, which have some local storage capacity, are modeled as finite queues fed by independent Poisson streams and the channel as a single exponential server. The performance objective is to avoid situations in which any of the queues is fully (blocking). The authors also consider systems in which the queues are fed by the server and the objective is to avoid situations in which any of the queues is empty (starvation), and a hybrid system, consisting of both types of queue. Many computer and communication systems fall within the framework of these models. The goal is to get a good control policy for these systems. The authors first prove certain structural properties of the optimal solution for the case N=2. These properties lead them to conclude that it is unlikely that a closed-form expression for the optimal policy could be found, but at the same time guide the derivation of a heuristic decision rule     

Delay analysis of a packet voice multiplexer by the ΣDi/D/1 queue

The performance of a statistical multiplexer whose inputs consist of a superposition of voice packet streams is studied. The delay for such a system is analyzed by solving the ΣD_i/ D/1 queue. The analytic method can be used to find the approximate mean delay for an arbitrarily large number of trunks and the approximate delay distribution when the number of trunks is less than 100. An efficient hybrid simulation of the packet voice multiplexer which can be used to find the delay distribution for a large number of trunks is presented. In addition, easily computable error bounds for the present approximation are provided, and the accuracy of the M/ D/1 approximation is investigated     

Performance analysis of nonblocking packet switch with input andoutput buffers

The performance of nonblocking packet switches such as the knockout switch and Batcher banyan switch for high-speed communication networks can be improved as the switching capacity L per output increases; the switching capacity per output refers to the maximum number of packets transferred to an output during a slot. The N×N switch with L=N was shown to attain the best possible performance by M.J. Karol et al. (1987). Here a N×N nonblocking packet switch with input and output buffers is analyzed for an arbitrary number of L such that 1⩽L⩽N. The maximum throughput and packet loss probability at input are obtained when N=∞     

A fast time slot assignment algorithm for TDM hierarchicalswitching systems

A fast (polynomial time) network-flow-based algorithm is presented for time slot assignment in time-division-multiplexing (TDM) hierarchical switching systems. For a nonblocking time-multiplexed central switch the algorithm produces a conflict-free time slot assignment for a given frame (whenever this is possible) on O(M ⁵) time, where M is the system size     

Design of coded CPFSK modulation systems for bandwidth and energyefficiency

Consideration is given to the problems related to the design of M-ary continuous-phase frequency-shift keying (CPFSK) systems with modulation index h=J/M, combined with eternal rate r binary convolution encoders. The following questions are raised and answered: (1) how should different encoder-modulator systems be compared and how can comparable systems be recognized from the system parameters, i.e. M, h, and r?; (2) what are the limits on the information rate per unit bandwidth, versus signal-to-noise ratio, when reliable transmission is required?; (3) how does one choose the system parameters M, h, and r when the overall system has to achieve a specified performance?; and (4) how does one design the external rate r binary convolutional encoder to put in front of the M-ary CPFSK modulation system with h=J/M ? A simple approximation for the bandwidth of a CPFSK signal is given and shown to be sufficiently accurate for system design purposes. The design of the external convolutional encoder is carried out in a novel way that leads to fewer states in the combined encoder-modulator system and thus yields improved performance for a given demodulation-decoding complexity compared to previous approaches for the design of coded CPFSK systems     

Nonuniform traffic analysis on a nonblocking space-division packetswitch

The nonuniform traffic performance on a nonblocking space division packet switch is studied. When an output link is simultaneously contended by multiple input packets, only one can succeed, and the rest will be buffered in the queues associated with each input link. given the condition that the traffic on each output is not dominated by individual inputs, this study indicates that the output contention involved by packets at the head of input queues can be viewed as an independent phase-type process for a sufficiently large size of the switch. Therefore, each input queue can be modeled by an independent Geom/PH/1 queueing process. Once the relative input traffic intensities and their output address assignment functions are defined, a general formulation can be developed for the maximum throughput of the switch in saturation. The result indicates under what condition the input queue will saturate. A general solution technique for the evaluation of the queue length distribution is proposed. The numerical study based on this analysis agrees well with simulation results     

The transient solution of time-dependent M/M/1 queues

The transient behavior of time-dependent M/M/1 queues is studied. The boundary probability function π₀(t), which is the probability that the queue is empty at time t, is shown with analyticity arguments to satisfy a Volterra-type integral equation. The boundary integral equation is derived, and a numerical algorithm is used to solve the integral equation and to find the expected queue size from π₀(t). The approach can be applied to many other types of time-dependent queues. Examples are given     

Repeated convolutional codes for high-error-rate channels

An error-correction scheme for an M-ary symmetric channel (MSC) characterized by a large error probability p_e is considered. The value of p_e can be near, but smaller than, 1-1/M, for which the channel capacity is zero, such as may occur in a jamming environment. The coding scheme consists of an outer convolutional code and an inner repetition code of length m that is used for each convolutional code symbol. At the receiving end, the m inner code symbols are used to form a soft-decision metric, which is passed to a soft-decision decoder for the convolutional code. The effect of finite quantization and methods to generate binary metrics for M>2 are investigated. Monte Carlo simulation results are presented. For the binary symmetric channel (BSC), it is shown that the overall code rate is larger than 0.6R₀, where R₀ is the cutoff rate of the channel. New union bounds on the bit error probability for systems with a binary convolutional code on 4-ary and 8-ary orthogonal channels are presented. For a BSC and a large m, a method is presented for BER approximation based on the central limit theorem     

The superposition of variable bit rate sources in an ATMmultiplexer

When variable-bit-rate sources are multiplexed in an asynchronous transfer mode (ATM) network, there arise queues with a particular form of correlated arrival process. Such queues are analyzed by exploiting a result expressing the distribution of work in system of the G/G/1 queue originally derived by V.E. Benes (1963). A simple alternative demonstration of this result is analyzed and extended to the case of fluid input systems. The result is applied first to a queue where the arrival process is a superposition of periodic sources (the Σ D_i/D/1 queue), and then to a variable-input-rate constant-output-rate fluid system. The latter is shown to model the so-called burst component of the considered superposition queuing process. The difference between this and the real queue, the cell component, can be evaluated by means of the results obtained for the Σ D_i/D/1 queue. The relative importance of these two components is explored with reference to the particular case of a superposition of on/off sources     

Bounds for abnormal binary codes with covering radius one

The normality of binary codes is studied. The minimum cardinality of a binary code of length n with covering radius R is denoted by K(n,R). It is assumed that C is an (n,M)R code, that is, a binary code of length n with M codewords and covering radius R. It is shown that if C is an (n,M)1 code, then it is easy to find a normal (n ,M)1 code by changing C in a suitable way, and that all the optimal (n,M)1 codes (i.e. those for which M=K(n,1)) are normal and their every coordinate is acceptable. It is shown that if C is an abnormal (n,M) code, then n⩾9, and an abnormal (9118)1 code which is the smallest abnormal code known at present, is constructed. Lower bounds on the minimum cardinality of a binary abnormal code of length n with covering radius 1 are derived, and it is shown that if an (n,M)1 code is abnormal, then M⩾96     

Velocity filters for multiple interference attenuation ingeophysical array data

The problem of velocity filtering a record of seismic data with the objective of extracting a desired signal by attenuating the coherent interferences traveling at different velocities is considered. A two-dimensional (N-input (N-M+1)-output) processing scheme is used where the (N-M+1) output traces are generated from the N-input traces by multichannel processing of overlapping subsets of M-input races. Each output is generated by using a vector of multichannel arrays filters designed to attenuate multiple coherent interference and random noise. The two-dimensional frequency-wavenumber expression corresponding to the proposed multiple-input-multiple-output processing scheme is derived so that it can be implemented using the two-dimensional fast Fourier transform. Two illustrative examples are included     

The effect of capture on performance of multichannel slotted ALOHAsystems

The author presents an exact analysis to evaluate the effect of capture on the multichannel slotted ALOHA protocol. The author derives the probabilities of the successful transmission. These probabilities are used to calculate the throughputs, average packet delays for both IFT (immediate-first-transmission) and delayed-first-transmission protocols and numerically compare the performance of the systems with and without capture. Numerical results show that when a quantitative capture restriction u is considered, in a multichannel system having a fixed total bandwidth, depending on parameter u and channel number M, an improved system performance such as the average channel utilization and average packet delay can be obtained