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.

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

1978 ◽  
Vol 15 (04) ◽  
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.

scholarly journals Mathematical Model of Call Center in the Form of Multi-Server Queueing System

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2877
Author(s):  
Anatoly Nazarov ◽  
Alexander Moiseev ◽  
Svetlana Moiseeva
Keyword(s):  
Distribution Function ◽  
Stationary Distribution ◽  
Service Time ◽  
Call Center ◽  
Queueing System ◽  
Optimization Problems ◽  
Arbitrary Distribution ◽  
Hyperexponential Distribution ◽  
Poisson Arrivals ◽  
Multi Server

The paper considers the model of a call center in the form of a multi-server queueing system with Poisson arrivals and an unlimited waiting area. In the model under consideration, incoming calls do not differ in terms of service conditions, requested service, and interarrival periods. It is assumed that an incoming call can use any free server and they are all identical in terms of capabilities and quality. The goal problem is to find the stationary distribution of the number of calls in the system for an arbitrary recurrent service. This will allow us to evaluate the performance measures of such systems and solve various optimization problems for them. Considering models with non-exponential service times provides solutions for a wide class of mathematical models, making the results more adequate for real call centers. The solution is based on the approximation of the given distribution function of the service time by the hyperexponential distribution function. Therefore, first, the problem of studying a system with hyperexponential service is solved using the matrix-geometric method. Further, on the basis of this result, an approximation of the stationary distribution of the number of calls in a multi-server system with an arbitrary distribution function of the service time is constructed. Various issues in the application of this approximation are considered, and its accuracy is analyzed based on comparison with the known analytical result for a particular case, as well as with the results of the simulation.

Modeling Bus Capacity for Bus Stops Using Queuing Theory and Diffusion Approximation

2021 ◽  
pp. 036119812110302
Author(s):  
Chao Wang ◽  
Weijie Chen ◽  
Yueru Xu ◽  
Zhirui Ye
Keyword(s):  
Approximation Method ◽  
Service Time ◽  
Diffusion Approximation ◽  
Coefficient Of Variation ◽  
Queuing Theory ◽  
Queuing Model ◽  
Bus Stop ◽  
Proposed Model ◽  
Bus Stops ◽  
Bus Service

For bus service quality and line capacity, one critical influencing factor is bus stop capacity. This paper proposes a bus capacity estimation method incorporating diffusion approximation and queuing theory for individual bus stops. A concurrent queuing system between public transportation vehicles and passengers can be used to describe the scenario of a bus stop. For most of the queuing systems, the explicit distributions of basic characteristics (e.g., waiting time, queue length, and busy period) are difficult to obtain. Therefore, the diffusion approximation method was introduced to deal with this theoretical gap in this study. In this method, a continuous diffusion process was applied to estimate the discrete queuing process. The proposed model was validated using relevant data from seven bus stops. As a comparison, two common methods— Highway Capacity Manual (HCM) formula and M/M/S queuing model (i.e., Poisson arrivals, exponential distribution for bus service time, and S number of berths)—were used to estimate the capacity of the bus stop. The mean absolute percentage error (MAPE) of the diffusion approximation method is 7.12%, while the MAPEs of the HCM method and M/M/S queuing model are 16.53% and 10.23%, respectively. Therefore, the proposed model is more accurate and reliable than the others. In addition, the influences of traffic intensity, bus arrival rate, coefficient of variation of bus arrival headway, service time, coefficient of variation of service time, and the number of bus berths on the capacity of bus stops are explored by sensitivity analyses.

scholarly journals Analysis of queue change of visitors and performace system in the Department of Population and Civil Regristation of Semarang City

2020 ◽  
Vol 202 ◽  
pp. 15005
Author(s):  
Sugito ◽  
Alan Prahutama ◽  
Dwi Ispriyanti ◽  
Mustafid
Keyword(s):  
Customer Satisfaction ◽  
Waiting Time ◽  
Public Service ◽  
Service Time ◽  
Service Sector ◽  
General Distribution ◽  
Queuing Systems ◽  
Queuing Model ◽  
The Public ◽  
Second Period

The Population and Civil Registry Office in Semarang city is one of the public service units. In the public service sector, visitor / customer satisfaction is very important. It can be identified by the length of the queue, the longer visitors queue this results in visitor dissatisfaction with the service. Queue analysis is one of the methods in statistics to determine the distribution of queuing systems that occur within a system. In this study, a queuing analysis as divided into two periods. The first period lasts from 2-13 March 2015, while the second period lasts November 16th to December 20th 2019. The variables used are the number of visitors and the service time at each counter in intervals of 30 minutes. The results obtained are changes in the distribution and queuing model that is at counter 5/6 and counter 10. The queuing model obtained at the second perideo for the number of visitors and the time of service with a General distribution. The average number of visitors who come in 30 minute intervals in the second period is more than the first period, this indicates an increase in visitors. The opportunity for service units is still small, the waiting time in the queue is getting smaller. This shows that the performance of the queuing system at the Semarang Population and Civil Registry Office is getting better.

scholarly journals M/M/c/N queuing systems with encouraged arrivals, reneging, retention and feedback customers

2018 ◽  
Vol 28 (3) ◽  
pp. 333-344 ◽  
Author(s):  
Bhupender Som ◽  
Sunny Seth
Keyword(s):  
System Size ◽  
Stationary System ◽  
Queuing Systems ◽  
Impatient Customers ◽  
Queuing Model ◽  
Special Cases ◽  
Multi Server ◽  
Measures Of Performance

Customers often get attracted by lucrative deals and discounts offered by firms. These, attracted customers are termed as encouraged arrivals. In this paper, we developed a multi-server Feedback Markovian queuing model with encouraged arrivals, customer impatience, and retention of impatient customers. The stationary system size probabilities are obtained recursively. Also, we presented the necessary measures of performance and gave numerical illustrations. Some particular, and special cases of the model are discussed.

scholarly journals Analysis of Multi-Server Queue with Self-Sustained Servers

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2134
Author(s):  
Alexander Dudin ◽  
Olga Dudina ◽  
Sergei Dudin ◽  
Konstantin Samouylov
Keyword(s):  
Three Dimensional ◽  
Optimal Choice ◽  
Arrival Process ◽  
Queuing Model ◽  
Numerical Result ◽  
Self Sufficiency ◽  
Server Queue ◽  
Markov Arrival ◽  
Markov Arrival Process ◽  
Multi Server

A novel multi-server vacation queuing model is considered. The distinguishing feature of the model, compared to the standard queues, is the self-sufficiency of servers. A server can terminate service and go on vacation independently of the system manager and the overall situation in the system. The system manager can make decisions whether to allow the server to start work after vacation completion and when to try returning some server from a vacation to process customers. The arrival flow is defined by a general batch Markov arrival process. The problem of optimal choice of the total number of servers and the thresholds defining decisions of the manager arises. To solve this problem, the behavior of the system is described by the three-dimensional Markov chain with the special block structure of the generator. Conditions for the ergodicity of this chain are derived, the problem of computation of the steady-state distribution of the chain is discussed. Expressions for the key performance indicators of the system in terms of the distribution of the chain states are derived. An illustrative numerical result is presented.

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