An extension of Erlang's loss formula

1976 ◽  
Vol 13 (3) ◽  
pp. 628-632 ◽  
Author(s):  
Ronald W. Wolff ◽  
Charles W. Wrightson
Keyword(s):  
Distribution Function ◽  
Stationary State ◽  
Loss System ◽  
Service Distribution ◽  
Poisson Arrivals ◽  
Loss Formula

A two-server loss system is considered with N classes of Poisson arrivals, where the service distribution function and server preferences are arrival-class dependent. The stationary state probabilities are derived and found to be independent of the form of the service distributions.

An extension of Erlang's loss formula

1976 ◽  
Vol 13 (03) ◽  
pp. 628-632 ◽  
Author(s):  
Ronald W. Wolff ◽  
Charles W. Wrightson
Keyword(s):  
Distribution Function ◽  
Stationary State ◽  
Loss System ◽  
Service Distribution ◽  
Poisson Arrivals ◽  
Loss Formula

A two-server loss system is considered with N classes of Poisson arrivals, where the service distribution function and server preferences are arrival-class dependent. The stationary state probabilities are derived and found to be independent of the form of the service distributions.

ON THE ADAN–WEISS LOSS MODEL HAVING SKILL-BASED SERVERS AND LONGEST IDLE ASSIGNMENT RULE

2015 ◽  
Vol 29 (2) ◽  
pp. 181-189 ◽  
Author(s):  
Babak Haji
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Monte Carlo Method ◽  
Gibbs Sampler ◽  
Service Time ◽  
Loss System ◽  
Multiplicative Constant ◽  
Assignment Rule ◽  
Poisson Arrivals

We consider a queueing loss system with heterogeneous skill based servers with arbitrary distributions. We assume Poisson arrivals, with each arrival having a vector indicating which of the servers are eligible to serve it. Arrivals can only be assigned to a server that is both idle and eligible. We assume arrivals are assigned to the idle eligible server that has been idle the longest and derive, up to a multiplicative constant, the limiting distribution for this system. We show that the limiting probabilities of the ordered list of idle servers depend on the service time distributions only through their means. Moreover, conditional on the ordered list of idle servers, the remaining service times of the busy servers are independent and have their respective equilibrium service distributions. We also provide an algorithm using Gibbs sampler Markov Chain Monte Carlo method for estimating the limiting probabilities and other desired quantities of this system.

Optimal Admission Controls for Erlang's Loss System with Phase-Type Arrivals

1996 ◽  
Vol 10 (3) ◽  
pp. 397-414 ◽  
Author(s):  
Ilze Ziedins
Keyword(s):  
Optimal Policy ◽  
Loss System ◽  
Standard Assumption ◽  
Threshold Policy ◽  
Phase Type ◽  
Reservation Policy ◽  
Poisson Arrivals ◽  
Trunk Reservation

It is known that a threshold policy (or trunk reservation policy) is optimal for Erlang's loss system under certain assumptions. This paper examines the robustness of this policy under departures from the standard assumption of Poisson arrivals and shows that the optimal policy has a generalized trunk reservation form.

scholarly journals MOVIMENTO BROWNIANO: APLICAÇÃO EM ESTRATÉGIAS DE BUSCA

2019 ◽  
Vol 5 (4) ◽  
pp. 0392-0402
Author(s):  
Matheus Dias Carvalho ◽  
Ricardo de Carvalho Falcão ◽  
Antonio Marcos de Oliveira Siqueira
Keyword(s):  
Distribution Function ◽  
Brownian Motion ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Metabolic Rate ◽  
Stationary State ◽  
Analytical Solutions ◽  
Random Processes ◽  
Graphical Form ◽  
Partial Differential

This article has elucidated information about Brownian Motion in the ring, something that is still little explored in the literature. In addition, the ideas of feed, metabolic rate and stochastic restart to the walker were added, features that have been gaining ground recently in the study of random processes. This paper structured partial differential equations governing this process for the immortal case of walker, and later found analytical solutions to these expressions. The representation of stationary state was also performed in graphical form, thus obtaining the distribution function of probability required. In order to briefly approach the walker in a deadly process, a graph was produced that presents the function between the number of steps taken by a walker before his death and his metabolic capacity.Este artigo elucidou informações a respeito do movimento browniano no anel, algo ainda pouco explorado na literatura. Além disso, foram adicionadas as ideias de alimentação, taxa metabólica e reinício estocástico ao caminhante, características que vem ganhando espaço recentemente no estudo de processos aleatórios. Esse artigo realizou a estruturação das equações diferenciais parciais que regem tal processo para o caso de um caminhante imortal, além de posteriormente encontrar soluções analíticas para estas expressões. A representação do estado estacionário do caminhante também foi realizada na forma gráfica, obtendo assim as funções distribuição de probabilidade requeridas. Com o intuito de abordar brevemente o caminhante em um processo mortal, foi produzido um gráfico que apresenta a função entre o número de passos dados por um caminhante antes de sua morte e sua capacidade metabólica.

M/G/1 queueing systems with returning customers

1989 ◽  
Vol 26 (01) ◽  
pp. 152-163 ◽  
Author(s):  
Betsy S. Greenberg
Keyword(s):  
Steady State ◽  
Laplace Transform ◽  
Single Channel ◽  
Queueing Systems ◽  
Service Distribution ◽  
Poisson Arrivals ◽  
General Service ◽  
Steady State Probabilities

Single-channel queues with Poisson arrivals, general service distributions, and no queue capacity are studied. A customer who finds the server busy either leaves the system for ever or may return to try again after an exponentially distributed time. Steady-state probabilities are approximated and bounded in two different ways. We characterize the service distribution by its Laplace transform, and use this characterization to determine the better method of approximation.

On the identification of Poisson arrivals in queues with coinciding time-stationary and customer-stationary state distributions

1983 ◽  
Vol 20 (04) ◽  
pp. 860-871 ◽  
Author(s):  
Dieter König ◽  
Masakiyo Miyazawa ◽  
Volker Schmidt
Keyword(s):  
Stationary State ◽  
Queueing Systems ◽  
Sufficient Conditions ◽  
Arrival Process ◽  
Loss Probabilities ◽  
Poisson Arrivals ◽  
Number Of Customers

For several queueing systems, sufficient conditions are given ensuring that from the coincidence of some time-stationary and customer-stationary characteristics of the number of customers in the system such as idle or loss probabilities it follows that the arrival process is Poisson.

M/G/1 queueing systems with returning customers

1989 ◽  
Vol 26 (1) ◽  
pp. 152-163 ◽  
Author(s):  
Betsy S. Greenberg
Keyword(s):  
Steady State ◽  
Laplace Transform ◽  
Single Channel ◽  
Queueing Systems ◽  
Service Distribution ◽  
Poisson Arrivals ◽  
General Service ◽  
Steady State Probabilities

Single-channel queues with Poisson arrivals, general service distributions, and no queue capacity are studied. A customer who finds the server busy either leaves the system for ever or may return to try again after an exponentially distributed time. Steady-state probabilities are approximated and bounded in two different ways. We characterize the service distribution by its Laplace transform, and use this characterization to determine the better method of approximation.

A Queueing Loss Model with Heterogeneous Skill Based Servers Under Idle Time Ordering Policies

2015 ◽  
Vol 52 (01) ◽  
pp. 269-277 ◽  
Author(s):  
Babak Haji ◽  
Sheldon M. Ross
Keyword(s):  
Service Time ◽  
Idle Time ◽  
Limiting Distribution ◽  
Loss System ◽  
Loss Model ◽  
Poisson Arrivals ◽  
Service Times ◽  
Ordering Policies

We consider a queueing loss system with heterogeneous skill based servers with arbitrary service distributions. We assume Poisson arrivals, with each arrival having a vector indicating which of the servers are eligible to serve it. An arrival can only be assigned to a server that is both idle and eligible. Assuming exchangeable eligibility vectors and an idle time ordering assignment policy, the limiting distribution of the system is derived. It is shown that the limiting probabilities of the set of idle servers depend on the service time distributions only through their means. Moreover, conditional on the set of idle servers, the remaining service times of the busy servers are independent and have their respective equilibrium service distributions.

Approximations in finite-capacity multi-server queues by Poisson arrivals

1978 ◽  
Vol 15 (4) ◽  
pp. 826-834 ◽  
Author(s):  
Shirley A. Nozaki ◽  
Sheldon M. Ross
Keyword(s):  
Service Time ◽  
Joint Distribution ◽  
Finite Capacity ◽  
Queuing Model ◽  
Average Delay ◽  
Service Distribution ◽  
Poisson Arrivals ◽  
Multi Server

An approximation for the average delay in queue of an entering customer is presented for the M/G/K queuing model with finite capacity. The approximation is obtained by means of an approximation relating a joint distribution of remaining service time to the equilibrium service distribution.

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