scholarly journals An Erlang Loss Queue with Time-Phased Batch Arrivals as a Model for Traffic Control in Communication Networks

2008 ◽  
Vol 2008 ◽  
pp. 1-14
Author(s):  
Moon Ho Lee ◽  
Sergey A. Dudin
Keyword(s):  
Communication Networks ◽  
Traffic Control ◽  
Batch Arrival ◽  
Arrival Process ◽  
Batch Arrivals ◽  
Poisson Arrival ◽  
Batch Arrival Of Customers ◽  
Single Epoch ◽  
Erlang Loss ◽  
Arbitrary Flow

A multiserver queueing model that does not have a buffer but has batch arrival of customers is considered. In contrast to the standard batch arrival, in which the entire batch arrives at the system during a single epoch, we assume that the customers of a batch (flow) arrive individually in exponentially distributed times. The service time is exponentially distributed. Flows arrive according to a stationary Poisson arrival process. The flow size distribution is geometric. The number of flows that can be simultaneously admitted to the system is under control. The loss of any customer from an admitted flow, with a fixed probability, implies termination of the flow arrival. Analysis of the sojourn time and loss probability of an arbitrary flow is performed.

scholarly journals Queing Theory, a Tool for Polio Eradication in Nigeria

2021 ◽  
pp. 123-133
Author(s):  
Raphael Ayan Adeleke ◽  
Ibrahim Ismaila Itopa ◽  
Sule Omeiza Bashiru
Keyword(s):  
Polio Eradication ◽  
Arrival Process ◽  
Health Departments ◽  
Batch Arrivals ◽  
Parallel Servers ◽  
Contagious Diseases ◽  
Poisson Arrival ◽  
Self Service ◽  
Using Data ◽  
Set Up

To curb the spread of contagious diseases and the recent polio outbreak in Nigeria, health departments must set up and operate clinics to dispense medications or vaccines. Residents arrive according to an external (not necessarily Poisson) Arrival process to the clinic. When a resident arrives, he goes to the first workstation, based on his or her information, the resident moves from one workstation to another in the clinic. The queuing network is decomposed by estimating the performance of each workstation using a combination of exact and approximate models. A key contribution of this research is to introduce approximations for workstations with batch arrivals and multiple parallel servers, for workstations with batch service processes and multiple parallel servers, and for self service workstations. We validated the models for likely scenarios using data collected from one of the states vaccination clinics in the country during the vaccination exercises.

scholarly journals Transient and Stationary Losses in a Finite-Buffer Queue with Batch Arrivals

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Andrzej Chydzinski ◽  
Blazej Adamczyk
Keyword(s):  
Batch Size ◽  
Buffer Size ◽  
Arrival Process ◽  
Time Interval ◽  
Finite Buffer ◽  
Finite Time Interval ◽  
Batch Arrivals ◽  
Batch Markovian Arrival Process ◽  
Buffer Overflows ◽  
Finite Buffer Queue

We present an analysis of the number of losses, caused by the buffer overflows, in a finite-buffer queue with batch arrivals and autocorrelated interarrival times. Using the batch Markovian arrival process, the formulas for the average number of losses in a finite time interval and the stationary loss ratio are shown. In addition, several numerical examples are presented, including illustrations of the dependence of the number of losses on the average batch size, buffer size, system load, autocorrelation structure, and time.

A study on the arrival process of lift passengers in a multi-storey office building

2011 ◽  
Vol 33 (4) ◽  
pp. 437-449 ◽  
Author(s):  
J-M Kuusinen ◽  
J Sorsa ◽  
M-L Siikonen ◽  
H Ehtamo
Keyword(s):  
Poisson Process ◽  
Time Of Day ◽  
Office Building ◽  
Arrival Process ◽  
Batch Arrivals ◽  
Arrival Times ◽  
Piecewise Constant ◽  
Practical Applications ◽  
Video Recordings ◽  
Traffic Simulations

This article presents a study on the process of how passengers arrive at lift lobbies to travel to their destinations. Earlier studies suggest that passengers arrive at the lift lobbies individually with exponentially distributed inter-arrival times, that is, according to a Poisson process. This study was carried out in a multi-storey office building. The data was collected using a questionnaire, digital video recordings and the lift monitoring system. The results show that, in the studied building, passengers arrive in batches whose size varies with the time of day and the floor utilization. In addition, the batch arrivals follow a time-inhomogeneous Poisson process with piecewise constant arrival rates. Practical applications: This article contributes to the basic understanding of passenger behaviour, and how people move around in buildings and arrive at the lift lobbies. It is proposed that the model for the passenger arrival process should take into account that passengers do not always arrive individually but also in batches. The passenger arrival process affects the design of elevators. It will also affect the passenger generation in building traffic simulations.

INFINITE-SERVER QUEUES WITH BATCH ARRIVALS AND DEPENDENT SERVICE TIMES

2012 ◽  
Vol 26 (2) ◽  
pp. 197-220 ◽  
Author(s):  
Guodong Pang ◽  
Ward Whitt
Keyword(s):  
Large Scale ◽  
Heavy Traffic ◽  
Arrival Rate ◽  
Arrival Process ◽  
Regularity Conditions ◽  
Time Varying ◽  
Performance Impact ◽  
Batch Arrivals ◽  
Infinite Server ◽  
Service Times

Motivated by large-scale service systems, we consider an infinite-server queue with batch arrivals, where the service times are dependent within each batch. We allow the arrival rate of batches to be time varying as well as constant. As regularity conditions, we require that the batch sizes be i.i.d. and independent of the arrival process of batches, and we require that the service times within different batches be independent. We exploit a recently established heavy-traffic limit for the number of busy servers to determine the performance impact of the dependence among the service times. The number of busy servers is approximately a Gaussian process. The dependence among the service times does not affect the mean number of busy servers, but it does affect the variance of the number of busy servers. Our approximations quantify the performance impact upon the variance. We conduct simulations to evaluate the heavy-traffic approximations for the stationary model and the model with a time-varying arrival rate. In the simulation experiments, we use the Marshall–Olkin multivariate exponential distribution to model dependent exponential service times within a batch. We also introduce a class of Marshall–Olkin multivariate hyperexponential distributions to model dependent hyper-exponential service times within a batch.

scholarly journals On optimal stochastic jumps in multi server queue with impatient customers via stochastic control

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Ali Delavarkhalafi
Keyword(s):  
Optimal Control ◽  
Complete Information ◽  
Queuing System ◽  
Arrival Process ◽  
Impatient Customers ◽  
Time Intervals ◽  
Poisson Arrival ◽  
Server Queue ◽  
Multi Server ◽  
Request Service

<p style='text-indent:20px;'>In this paper, a queuing system as multi server queue, in which customers have a deadline and they request service from a random number of identical severs, is considered. Indeed there are stochastic jumps, in which the time intervals between successive jumps are independent and exponentially distributed. These jumps will be occurred due to a new arrival or situation change of servers. Therefore the queuing system can be controlled by restricting arrivals as well as rate of service for obtaining optimal stochastic jumps. Our model consists of a single queue with infinity capacity and multi server for a Poisson arrival process. This processes contains deterministic rate <inline-formula><tex-math id="M1">\begin{document}$ \lambda(t) $\end{document}</tex-math></inline-formula> and exponential service processes with <inline-formula><tex-math id="M2">\begin{document}$ \mu $\end{document}</tex-math></inline-formula> rate. In this case relevant customers have exponential deadlines until beginning of their service. Our contribution is to extend the Ittimakin and Kao's results to queueing system with impatient customers. We also formulate the aforementioned problem with complete information as a stochastic optimal control. This optimal control law is found through dynamic programming.</p>

Erlang loss queueing system with batch arrivals operating in a random environment

2009 ◽  
Vol 36 (3) ◽  
pp. 674-697 ◽  
Author(s):  
Che Soong Kim ◽  
Alexander Dudin ◽  
Valentina Klimenok ◽  
Valentina Khramova
Keyword(s):  
Random Environment ◽  
Queueing System ◽  
Batch Arrivals ◽  
Erlang Loss

The departure process from a queueing system

1976 ◽  
Vol 80 (2) ◽  
pp. 283-285 ◽  
Author(s):  
F. P. Kelly
Keyword(s):  
Queueing System ◽  
Arrival Process ◽  
Single Server ◽  
Departure Process ◽  
Common Distribution ◽  
Poisson Arrival ◽  
Queue Discipline ◽  
Common Distribution Function ◽  
Image Position ◽  
Poisson Arrival Process

Consider a single-server queueing system with a Poisson arrival process at rate λ and positive service requirements independently distributed with common distribution function B(z) and finite expectationwhere βλ < 1, i.e. an M/G/1 system. When the queue discipline is first come first served, or last come first served without pre-emption, the stationary departure process is Poisson if and only if G = M (i.e. B(z) = 1 − exp (−z/β)); see (8), (4) and (2). In this paper it is shown that when the queue discipline is last come first served with pre-emption the stationary departure process is Poisson whatever the form of B(z). The method used is adapted from the approach of Takács (10) and Shanbhag and Tambouratzis (9).

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