Analysis of finite-buffer state-dependent bulk queues

<p>In this paper, we consider a general state-dependent finite-buffer bulk queue in which the rates and batch sizes of arrivals and services are allowed to depend on the number of customers in queue and service batch sizes. Such queueing systems have rich applications in manufacturing, service operations, computer and telecommunication systems. Interesting examples include batch oven processes in the aircraft and semiconductor industry; serving of passengers by elevators, shuttle buses, and ferries; and congestion control mechanisms to regulate transmission rates in packet-switched communication networks. We develop a unifying method to study the performance of this general class of finite-buffer state-dependent bulk queueing systems. For this purpose, we use semi-regenerative analysis to develop a numerically stable method for calculating the limiting probability distribution of the queue length process. Based on the limiting probabilities, we present various performance measures for evaluating admission control and batch service policies, such as the loss probability for an arriving group of customers and for individual customers within a group. We demonstrate our method by means of numerical examples.</p>

Retrial queue M/M/N with impatient customer in the orbit

In the paper, the retrial queueing system of M/M/N type with Poisson flow of events and impatient calls is considered. The delay time of calls in the orbit, the calls service time and the impatience time of calls in the system have exponential distribution. Asymptotic analysis method is proposed for the solving problem of finding distribution of the number of calls in the orbit under a system heavy load and long time patience of calls in the orbit condition. The theorem about the Gauss form of the asymptotic probability distribution of the number of calls in the orbit is formulated and proved. Numerical illustrations, results are also given

Optimal estimation of the states of synchronous generalized flow of events of the second order under its complete observability

We consider the optimal estimation problem of the states of synchronous generalized flow of events of the second order with two states; it is one of the mathematical models for an incoming stream of claims (events) in digital integral servicing networks and which is related to the class of Markov chains. The observation conditions for this flow are such that each event is accessible to observation. We offer the optimal estimation algorithm for the flow states, where the decision about the flow state is made by criterion of a posteriori probability maximum. The results of the analytical calculations of a posteriori probability and the simulation experiments with numerical results are presented

Optimal state estimation of semi-synchronous event flow of the second order under its complete observability

We consider the optimal estimation problem for the states of a semi-synchronous event flow of the second order with two states; it is one of the adequate mathematical models for an incoming stream of claims (events) in modern digital integral servicing networks, telecommunication systems, satellite communication networks. We find an explicit form for posterior probabilities of the flow states. The decision about the flow state is made with the maximal a posteriori criterion

Retrial queueing system of MMPP/M/2 type with impatient calls in the orbit

In the paper, the retrial queueing system of MMPP/M/2 type with input MMPP-flow of events and impatient calls is considered. The delay time of calls in the orbit, the calls service time and the impatience time of calls in the orbit have exponential distribution. Asymptotic analysis method is proposed for the solving problem of finding distribution of the number of calls in the orbit under a system heavy load and long time patience of calls in the orbit condition. The theorem about the Gauss form of the asymptotic probability distribution of the number of calls in the orbit is formulated and proved. Numerical illustrations, results are also given

Asymptotic analysis methods for multi-server retrial queueing systems

In this paper, we consider a multi-server retrial queueing system of type M/M/N. We propose the asymptotic methods for analysis of the system under long delay and heavy load conditions. Application areas of each method are defined and numerical examples are given

Assembly and Magnetic Bistability of Mn 3

Magnetic nanoparticles are encapsulated within hollow carbon nanofibers. The density and orientation of the guest Mn3O4 nanoparticles depend crucially on the internal structure of the host carbon nanocontainer, which enables tuning functional magnetic properties of the composite material.Financial support of the Royal SocietyS

Distribution Parameters Estimation in Recurrent Synchronous Generalized Doubly Stochastic Flow of the Second Order

We solve the estimation problem of the probability density parameters of the inter-event interval duration in a synchronous generalized flow of the second order, which can be used as a powerful mathematical model for the arrival processes in queuing systems and networks. The explicit form of the parameter estimates is determined by the method of moments on the basis of observations of the doubly stochastic flow under the recurrence conditions that are formulated in terms of the joint probability density of the durations of two adjacent inter-event intervals. The quality of the estimates is established by using the model, reproducing the flow behavior under conditions of complete observability