A model for fast switching transients in power systems: the nearzone concept

The author presents a simple time-domain model which makes it possible to predict the order of magnitude of the highest di/ dt values generated by closing switches in electrical power systems. The model is based on traveling-wave analysis. It is demonstrated that two different approaches must be applied, according to whether (a) the closing time, T_s, of the switch is faster than twice the traveling time to the first reflection point or (b) T_s is much slower. Under condition (b) the well-known quasistationary approach di/dt_max=U₀/L can be used, where U₀ is the switched voltage and L is the self-inductance of the line between the stray capacitances located to the left and the right of the switching device. Under condition (a) a new formula must be applied: di/dt _max≈2 U₀/ZT_s, where Z is the line impedance of the line in which the switching device is installed and T_s is the time during which the voltage across the switch collapses from U₀ to zero. Experimental results are given from both fast and slow closing switches     

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     

Numerical evaluation of parabolic cylinder functions

The numerical evaluation of the parabolic cylinder functions D _p(z) in two cases is described. Case I is for the argument z=xe^-iπ/4, with x real, and the order p=-1/2+iy, with y real. Case II is for z arbitrary, but p an integer. These cases are of special importance in the analysis of wave scattering from a parabolic cylinder. Expressions for D_p(z) are presented which are numerically accurate and efficient     

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     

The M/G/1 queue with permanent customers

The authors examine an M/G/1 FCFS (first come, first served) queue with two types of customers: ordinary customers, who arrive according to a Poisson process, and permanent customers, who immediately return to the end of the queue after having received a service. The influence of the permanent customers on queue length and sojourn times of the Poisson customers is studied using results from queuing theory and from the theory of branching processes. In particular, it is shown that, when the service time distributions of the Poisson customers and all K permanent customers are negative exponential with identical means, the queue length and sojourn time distributions of the Poisson customers are the (K+1)-fold convolution of those for the case without permanent customers     

Optimal pump wavelength in the4I15/2-4I13/2 absorption band for efficient Er3+-doped fiberamplifiers

The authors report the measured gain of a highly efficient erbium-doped fiber amplifier pumped at wavelengths between 1.46 and 1.51 μm. The optimal pump wavelength, λ_opt, was determined to be 1.475 μm. At this wavelength, the maximum gain coefficients for signals at 1.531 and 1.544 μm were 2.3 and 2.6 dB/mW, respectively. At λ_opt, high gains ranging from 32 dB at pump power P_p=20 mW up to 40 dB at P _p=80 mW were obtained. These modest pump powers are within the capabilities of currently available 1.48-μm diode lasers. The width about λ_opt for 3-dB gain variation exceeded 27 nm for P_p=10 mW and 40 nm for P_p >20 mW. With this weak dependence on pump wavelength, single-longitudinal-mode lasers do not have a significant advantage over practical Fabry-Perot multimode pump lasers     

The convexity of loss rate in an Erland loss system and sojourn inan Erlang delay system with respect to arrival and service rates

The Erlang loss system is a system in which customers arriving in a Poisson stream of arrival rate λ are served by a group of n servers, with a mean service time of 1/μ. Arrivals that find all servers busy are blocked and cleared from the system. The Erlang delay system is a system in which customers who find all servers busy wait in a queue until served by the first available server. Proofs of joint-convexity results in the Erlang delay system and Erlang loss system are presented, using induction on the number of servers and making use of the relation between the Erlang B and the Erlang C functions. The approach leads to a straightforward algebraic analysis of the properties of the performance measures of interest and avoids cumbersome manipulations     

AlGaAs and GaAsP high-power ultrafast p+-n-n+diodes based on heterojunctions and a graded-gap base

The authors present a theoretical model of power p⁺-n-n ⁺ diodes with a graded-gap base and either homojunctions (GB) or heterojunctions (HGB), and numerical calculations of static and dynamic characteristics of AlGaAs (GaAsP) based structures. It is shown that HGB diodes will exhibit characteristics and properties significantly better than those of simple (homojunctions plus uniform base) GaAs and Si diodes. For example, the forward voltage drop in a high-voltage (W/L_p=13) high-frequency (t_rr=25 ns) HGB diode will be 50% and 300% smaller than the drop in, respectively, simple GaAs and Si diodes with the same W/L_p and t_rr. Other significant projected improvements include operation up to 450°C, an order of magnitude reduction in the reverse current, and a 50% increase in the breakdown voltage     

Cyclic-service systems with probabilistically-limited service

An asymmetric cyclic-service system with a probabilistically limited (PL) service policy is analyzed. In such a service policy, the maximum number of customers served at a queue during a server visit is determined by a probability which is independent of system states. Exhaustive, limited-k, and Bernoulli services are special cases of the PL policy. Customer service times and changeover times have general distribution. A numerical technique based on discrete Fourier transforms is proposed to solve for the queue-length distributions. Thus, the waiting and response-time distribution are obtained. A set of numerical examples is presented to validate the approach     

High-frequency characterization of heterojunction bipolartransistors using numerical simulation

The high-frequency performance of semiconductor devices is estimated using a small-signal numerical calculation based on drift-diffusion equations. In particular, unity current gain frequency in the common-emitter configuration (f_T) and maximum frequency of oscillation (f_max) are calculated for a heterojunction bipolar transistor. f_max is calculated from numerically obtained y parameters using formulas for maximum available gain, Mason's invariant (U), and a passivity criterion. They all give the same value for f_max. The influence of extrinsic and intrinsic base resistance on f_max is investigated for one device design. It is also found that a frequency used approximation formula for f_max is inaccurate, especially at higher current levels     

Retrials and balks (queueing)

An overloaded service system may reject customers if it has no queue to store them. In practice, rejected customers return later to make retrials and may not leave permanently (balk) until several retrials fail. A single-server system with Poisson arrivals is examined in which rejected customers balk or make retrials according to a simple probabilistic model. Customer service times are independent random variables, all with the same given distribution function b(t). The stationary probability distribution for the number of customers waiting to make retrials satisfies a complicated functional equation. The solution is elusive in general but can be obtained for special b(t) (exponential distribution) or special values of model parameters. When the solution cannot be found, bounds on the fraction of customers served can be obtained     

Queueing analyses of traffic access control strategies withpreemptive and nonpreemptive disciplines in wideband integrated networks

A multiserver queueing model of access control strategies for a wideband integrated services digital network (ISDN) is considered. There are two types of service requests (SRs): Type 1 SR requires b servers (basic bandwidth units, BBUs) of the c available servers, while Type 2 SR requires a single server. Both types of SRs are queuable in two separate infinite-size buffers. A Type 1 SR is allowed to seize d(⩽b) servers at first and then acquire additional servers as they become available to meet the original requirement of b servers. The arrival processes of both types of SRs are Poisson and the service times are exponentially distributed with mean b/dμ₁ and 1/μ₂ for Type 1 SR and Type 2 SR, respectively. Preemptive and nonpreemptive priority disciplines with movable boundary are analyzed using the Neuts' matrix-analytic approach. Numerical examples of the queue length distribution and the mean waiting time of the SRs are presented     

Bounds on the entropy series

Upper bounds on the entropy of a countable integer-valued random variable are furnished in terms of the expectation of the logarithm function. In particular, an upper bound is derived that is sharper than that of P. Elias (ibid., vol.IT-21, no.2, p.194-203, 1975), for all values of E_p(log). Bounds that are better only for large values of E_p than the previous known upper bounds are also provided     

Analysis of a correlated queue in a communication system

A family of queues is studied for which the service time B_n of customer n and the interarrival time I_n between customers n-1 and n exhibit some sort of proportionality. The focus is on dependencies that arise naturally in the context of communication systems, where the finite speed of the communication links constrains the amount of data that can be received in a given time interval. The simple case of a deterministic proportionality relation between the service time of a customer and its preceding interarrival time is considered. This is extended to allow the addition of an independent, generally distributed overhead to the service time of each customer. Several models that capture the ON-OFF behavior of communication links in packet networks are considered. In all cases, expressions for the delay experienced by a packet in the system are provided. Numerical examples illustrate the impact of dependencies through comparison with less accurate models. The results should be of relevance to environments other than communication as well     

An M/G/1 vacation model of an FDDI station

The author defines and analyzes an M/G/1 vacation model that can be used to describe a single station in the fiber distributed data interface (FDDI). The M/G/1 model uses a service discipline called the exhaustive limited with limit variation discipline. According to this discipline, the server provides service until either the system is emptied or a randomly chosen limit of l frames has been served. The server then goes on a vacation before returning to service the queue again. The model can be used to gain insight into how the varying (timer-controlled) limit on the number of frames that can be transmitted during token visit at a station affects the mean waiting time in the timed-token protocol of FDDI. The analytical results of the M/G/1 vacation model are applied to an FDDI simulation example     

Theory and operation of a GaAs/AlGaAs/InGaAs superlatticephototransistor with controlled avalanche gain

The principle of operation of a bipolar transistor with controlled multiplication of one type of carrier is outlined. The ideal device, with a few periods of a staircase superlattice in the base-collector depletion region, has high current outputs at extremely low bias voltages and high current gains. The principle is experimentally demonstrated in a GaAs/AlGaAs/InGaAs phototransistor where three periods of a periodic pseudomorphic structure, in which electrons should predominantly multiply, are included in the collector depletion region. Independent measurements of the electron and hole avalanche multiplication rates, M_n and M_p, in these structures confirm that M_n/M_p M_n/M_p and α/β are ~2-4, depending on bias voltage. The observed photocurrent characteristics agree reasonably well with Monte Carlo calculations made to simulate the transport of electrons through the collector region. Measured optical gains are as high as 142 in an n-p-n phototransistor with a 2000-Å p-base region     

The generalizedD [X] /D/1 queue: A flexible computer communications model

A generalization of theD ^[X] /D/1 queue is investigated, where independent and identically distributed (i.i.d) batches of customers arrive at a single-server queue periodically. The service requirement of a customer is a fixed constant equal for all the customers. In the time between two successive arrivals, the server can accommodate exactlyK1 customers. The queue size and the waiting time distributions for the infinite buffer queue are derived. Important numerical aspects are addressed and simple approximations for light and heavy traffic for various values ofK and Poisson distributed batches are proposed. Finally, the analysis for the finite queue is highlighted and its blocking probability derived.     

Wavelength dependence of 1/f noise in the light output oflaser diodes: an experimental study

The optical power emitted by a monomode GaAlAs laser is filtered with a monochromator. The 1/f noise in the filtered emission is found to be directly dependent on the noncoherent emission, such as S_pαP_nc^m. Here s_p is the spectral density of the 1/f fluctuations, P_nc is the average noncoherent power, m=3/2 under spontaneous emission, and m=4 in the superradiation and laser regions. Study of the 1/f noise in the optical power in a band centered at the laser wavelength and with variable bandwidth shows three operating regions. (1) LED region (at low currents): the fluctuations with a 1/f spectrum are uncorrelated in wavelength. (2) Superradiation region (at currents close to the threshold): the fluctuations are correlated. (3) Laser region: the 1/f noise apparently is dominated by noncoherent emission within a small optical band around the laser wavelength     

Robust decoding for timing channels

To transmit information by timing arrivals to a single-server queue, we consider using the exponential server channel's maximum likelihood decoder. For any server with service times that are stationary and ergodic with mean 1/μ seconds, we show that the rate e ^-1μ nats per second (capacity of the exponential server timing channel) is achievable using this decoder. We show that a similar result holds for the timing channel with feedback. We also show that if the server jams communication by adding an arbitrary amount of time to the nominal service time, then the rate e^-1μ₁μ₂/(μ₁+μ ₂) nats per second is achievable with random codes, where the nominal service times are stationary and ergodic with mean 1/μ₁ seconds, and the arithmetic mean of the delays added by the server does not exceed 1/μ₂ seconds. This is a model of an arbitrarily varying channel where the current delay and the current input can affect future outputs. We also show the counterpart of these results for single-server discrete-time queues