A queueing system with K servers operates in the following manner. When the system is empty, arriving customers are attended by only one server. A set of forward threshold values is defined so that at epochs at which the number of customers in the system exceeds a forward threshold value an extra server is added. Similarly, a set of reverse threshold values is defined so that at epochs at which the number of customers in the system becomes less than a reverse threshold value one server is removed. The forward and reverse threshold values are assumed to be different. Closed-form occupancy distribution and mean delay of customers in the system are obtained by the Green's function method.

A mobile cellular communication system is considered. The calls arriving at the base station of each cell are modeled by a queueing system with two arrival streams. Stream 1 (also called class 1) arrivals are those calls in progress that are handed over to the cell from other cells, and class a arrivals are those calls that are originating in the cell. The guard channel scheme is considered in which arriving calls are indiscriminately assigned channels within a cell as long as the number of busy channels in the cell is below a predefined threshold. When this number reaches the threshold, only arriving class 1 calls are assigned channels immediately; arriving class 2 calls are queued. When all the channels are busy, then arriving class 1 calls are lost while class 2 calls continue to be queued. The system is analysed by a generating function method which utilizes the structure of the model to give a very concise solution.>

The performance analysis of a synchronous finite buffer ATM cell multiplexer with heterogeneous or homogeneous bursty sources and multiple servers is considered. A novel solution technique, based on the method of compensation, is formulated that reduces the problem of obtaining the ergodic state distribution and the associated performance measures to (1) the determination of the ergodic Green's density matrix for an associated homogeneous process defined on an infinite strip and (2) the solution of a system of linear equations whose order depends only on the number of sources. An important feature of the approach is that it facilitates a parametric analysis with respect to the buffer size. Several numerical examples are provided to illustrate the theory. Simulation results are also used to validate the theoretical analysis.>

Many telecommunication systems with time-critical requirements use a preempt-resume clocked schedule. An approximation to the ergodic distribution of the time to completion of a low-priority task is obtained by treating the priority service time distribution as the limit of compound Poisson distributions. Explicit formulas for the mean and variance that are highly accurate are given. For random clocked loads, a stochastic bound is provided for the discrepancy between the exact and approximate distributions. For deterministic clocked loads, sample path bounds are found. Simulation results are given to demonstrate the accuracy of the model.>

Shot noise, represented by a series of impulses with Poisson distribution in time, and with arbitrary time-independent amplitude distribution, is sent through an RC integrator. Time-dependent statistics of the output are investigated by means of an integro-differential equation describing the statistical flow. The exact second-order probability density of the output is obtained. The time-dependent Edgeworth series for zero initial output is exhibited, and is seen to bear a simple relation to the familiar equilibrium Edgeworth series. Results are shown to reduce to those of the Fokker-Planck equation describing integrated "white" noise as the frequency with which impulses arrive becomes infinite,

Two channels carry noise waveforms,N_0 (t) + N_1 ( t)andN_0 (t) + N_2 (t), whereN_0 (t)is a common narrow-band Gaussian noise andN_1 (t)andN_2 (t)are independent narrow-band Gaussian noises associated with each channel. The outputs of each channel are sent through detectors whose outputs,F(x, y), are identical homogeneous functions of the components,xandy, of their inputsN, whereN(t) = x(t) \cos \omega_0 t + y(t) \sin \omega_0 t. LetR_{12}(\tau)be the normalized cross-correlation function of the two detector outputs. It is shown that to determineR_{12}(\tau)it suffices to know the normalized auto-correlation functionR_0(\tau)of the output of a single such detector when the input isN_0(t); i.e., ifR_0(\tau) = G(\sigma_0^2, p(\tau))wherep(\tau)and\sigma_0are the normalized auto-correlation function and rms of either component ofN_0, then it is shown thatR_{12}(\tau) = G(\sigma_0^2, Z_{\rho}(\tau))whereZ = [\{1 + (\sigma_1^2/\sigma_0^2)\} \{(1 + (\sigma_2^2/\sigma_0^2)\}]^{-\frac{1}{2}}.