Probability-generating function

About: Probability-generating function is a research topic. Over the lifetime, 752 publications have been published within this topic receiving 9361 citations.

Constant hardware delay in integrated switching elements with multiserver output queues

Abstract: The authors consider an integrated switching element with a shared buffer memory and a constant hardware delay. This hardware delay is caused by the hardware operations required to process the routing information of incoming cells. A general uncorrelated cell arrival process in the switch, an independent and uniform routing process of cells from the inlets to the outlets of the switch and a first-come-first-served queueing discipline are assumed. The performance of the switching element is evaluated by means of an analytical technique based on an extensive use of probability generating functions. Explicit expressions for the probability generating functions, the mean values, the variances and the tail probabilities of the occupancy and the cell delay of the switch are obtained. Numerical examples show that the hardware delay has an important impact on the switch performance.

Probability density function isolating device, probability density function isolating method, test device, bit error ratio measuring device, electronic device, and program

Abstract: Provided is a probability density function isolating device for isolating a predetermined component from a given probability density function. The device includes: a region conversion unit for receiving a probability density function and converting the probability density function into a frequency region spectrum; and a definite component calculation unit for multiplying a first null frequency of the frequency region spectrum by a multiplication coefficient based on a distribution type of a definite component contained in the given probability density function so as to calculate a peak-to-peak value of the probability density function of the definite component.

Sum of Discrete i.i.d. Random Variables and Its Application to Cooperative Spectrum Sensing

Abstract: In this paper, we derive the probability mass function (PMF) and the cumulative mass function (CMF) of the sum of discrete independent and identically distributed random variables. As an application of the PMF and CMF, we analyze the missed-detection, false-alarm, and overall error probabilities of cooperative spectrum sensing with any numbers of quantization levels and any quantization thresholds in a closed form. Computer simulation results match the analysis perfectly. In addition, centralized and distributed threshold selections are discussed.

On functions having non-negative derivatives at the origin

Abstract: Functions which have non-negative derivatives at the origin play an important role in the theory of probability. The moment generating functions of symmetric distributions and the probability generating functions of lattice distributions are examples of such functions which are most commonly used. In the present note, we give two theorems on the properties of such functions. These theorems have interesting applications in the theory of decomposition of distribution functions which is known as "arithmetic of distributions." First we give the following definition: DEFINITION. Let f(x) be a function of the real variable x which has finite derivatives of all orders

Unreliable bulk queueing model with optional services, Bernoulli vacation schedule and balking

Abstract: This paper deals with MX/G/1 queueing system in which arriving units join a single waiting line. Server provides the first essential service and one of the optional services among m available optional services, to all arriving units. After completion of both phases of services of each unit the server may take optional vacation with probability p. It is assumed that during any phase of service, server may stop working due to random failure and is sent for repair. Further it is assumed that arriving units may balk from the system when server is busy, vacation and under repair with probability -b = 1 – b. Using the probability generating functions we derive the queue size distribution at different time points as well as waiting time distribution. Finally numerical illustration is provided to analyse the sensitivity of different parameters on various performance measures.