# Single-server and multi-server waiting line models. Publications (complete list)

An arriving batch, finding server busy, enters an orbit.

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Otherwise one customer from the arriving batch enters for service immediately while the rest join the orbit. The customers from the orbit try to reach the server subsequently and the inter-retrial times are exponentially distributed. Additionally, at each service completion epoch, two different search mechanisms are switched-on. Thus, when the server is single-server and multi-server waiting line models, a competition takes place between primary customers, the customers coming by retrial and the two types of searches.

It is assumed that if the type II search reaches the service facility ahead of the rest, all customers in the orbit are taken for service simultaneously, while in the other two cases, only a single customer is qualified to enter the service. We assume that the service times of the four types of customers namely, primary, repeated and those by the two types of searches are arbitrarily distributed with different distributions. Steady state analysis of the model is performed.

Alexander Dudin, T. Deepak, Varghese C. Joshua, Achyutha Krishnamoorthy, Vladimir Vishnevsky Reliability Analysis of a Two-Server Heterogeneous Unreliable Queueing System with a Threshold Control Policy Heterogeneous servers which can differ in single-server and multi-server waiting line models speed and reliability are getting more popular in modeling of modern communication systems.

For a two-server queueing system with unreliable servers the allocation of customers between the servers is performed via a threshold control policy which prescribes to use the fastest server whenever it is free and the slower one only if the number of waiting customers exceeds some threshold single-server and multi-server waiting line models depending on the state of faster server. The main task of the paper consists in reliability analysis of the proposed system including evaluation of the stationary availability and reliability function.

The effects of different parameters on introduced reliability characteristics are analyzed numerically.

### Solving performance models based on basic queueing theory formulas

Upon arrival, an incoming call either occupies the server if it is idle or joins an orbit if the server is busy. From the orbit, an incoming call retries to occupy the server and behaves the same as a fresh incoming call. The server makes an outgoing call in its idle time. Our contribution is to derive the asymptotics of the number of calls in retrial queue under the conditions of high rate of making outgoing calls and low rate of service time of outgoing calls.

If both servers are able to provide the service, they serve a customer in parallel, independently of each other. The service times at the servers have PH-type Phase-type distributions.

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An arriving breakdown is directed to the first server with some probability and to the second server with complementary probability. After a breakdown occurrence a server fails and the repair period starts immediately.

A customer, whose service is interrupted by the breakdown, goes to another server if it is idle, or enters the queue otherwise We derive a condition for the stable operation of the system, calculate its stationary distribution and base performance measures. Illustrative numerical examples are presented.

In more detail we focus on the distributions of the total capacity of customers in the different elements of the queue waiting line, service and entire system and provide approximate expressions for the corresponding characteristic functions. To verify the goodness of the proposed approximation, several sets of simulations have been carried out, considering discrete and continuous distributions of the customer capacity and using the Kolmogorov distance as a measure of similarity.

Ekaterina Lisovskaya, Svetlana Moiseeva, Michele Pagano On the Problems of Queues in Mixed Type Queuing Systems with Random Quantity of Sources and Size-Limited Queues The article proposes the technique to investigate the behavior of the moments of numerical characteristics of mixed-type queuing system with schwarzes brett bekanntschaften random number of sources upon the change of demands input stream intensity and size-limited queues based on the calculation of boundary values of the number of servicing devices at which the mean squared deviation MSD of the investigated quantity does not exceed its mathematical expectation.

For the single-server and multi-server waiting line models time the linear nature of behavior of boundary values of the number of service facilities with the change of the given intensity of demands input stream is determined numerically. The article also considers various types of queues arising in queuing systems. It is assumed that some demands do not acquire the item after service completion and order replenishment lead time single-server and multi-server waiting line models a positive random variable.

The exact and approximate methods are developed for calculation of joint distributions of the inventory level and number of customers in the system. The formulas for the system performance measures calculation are given as well. The high accuracy of formulas are confirmed by numerical experiments. The problem of choosing the optimal server rate to minimize the total cost is solved. The method of elapsed service time and the method of residual service time are considered using asymptotic approach under the condition of unlimited growing number of sources.

### Frau sucht sexsüchtigen mann

It is proved, as it was expected, that basic characteristics of the system, such as the stationary probability distribution of the server states and the asymptotic average of the normalized number of customers in the system are the same and do not depend on the applied method. The total volume of customers accepted by the system schwangerschaft single frau upper bounded by a finite constant system capacity M.

We give renewal-based approximations for a number of important stationary parameters of the system, in particular, the mean lost volume. For a large M, the loss is typically a rare event, and Single-server and multi-server waiting line models Monte-Carlo method is time-consuming to obtain accurate estimate of the loss probability in an acceptable simulation time.

We apply splitting method to speed-up estimation of the parameters by simulation.

In particular, we focus on heavy load. We perform simulations for different values of capacity, different volume size distributions, including heavy- and light-tailed distributions, and also for different values of traffic intensity. Evsey Morozov, Lyubov Potakhina Research of Heterogeneous Queueing System SM M One of the modifications of the mathematical models used to describe processes in multi-service communication networks and telecommunication systems is the queueing system with heterogeneous servers.

As a rule, for simulation of such processes the system with non-Poisson input flows is used. We consider the queuing system with infinite number of servers single-server and multi-server waiting line models n different types and exponential service time. Investigation of n-dimensional stochastic process characterizing the number of occupied servers of different types is performed using the initial moments method.

## Mehrere MID-Server bereitstellen

For the truncated model of Q t stationary probabilities are written in explicit vector-matrix form. The service time at each stage is given by an arbitrary flirten frankreich function.

The method of limiting decomposition is used for the study. As a result of the research, stationary distributions of the number of customers at each stage of the system are found.

The obtained analytical results are compared with the asymptotic ones which were obtained in previous papers. For such combination, we determine the steady-state loss probability and distribution of number of demands present in each system of the combination. We gothic singles saarland ways of preventing the losses within the framework of queueing theory; relevant simulation experiments are carried out.

### Deutschland single-server and multi-server waiting line models

Approximation methods for loss probability in the nodes of multiserver queueing system without buffers are investigated. The paper offers to approximate the loss probability in the node with n channels by steady-state probability in the state n of relating infinite-server queueing systems. We develop an analytical-statistical technique of optimal channel distribution over the nodes in networks with fractal traffic which is based on such approximation.

The example of the method application is provided. The developed method could be used by engineers designing the telecommunication networks. Vladimir N. Zadorozhnyi, Tatiana R.