On a Multi-Channel Retrial Queueing System

Pryshchepa, O. V.; Lebedev, Eugene

doi:10.1007/s10559-017-9945-3

Cited by 3 publications

(4 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…b. Update the value of for the state in Zone IIIa using equation (6). c. Update the value of for the state in Zone IIIb using equation (7). d. Update the value of for the state in Zone IV using equation (8).…”

Section: Modelingmentioning

confidence: 99%

“…Xiong and Altiok [5] studied multiserver queuing systems to model the maximum limit of waiting time available in an information processing system. Koroliuk et al [6] and Pryshchepa et al [7], for example, examine the problem of the multiserver queuing phenomenon in telecommunications issues where there is retrial arrival. Sultan et al [8,9] examined the problem of a multiserver system where arrivals occur in batches using the Montecarlo simulation method.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modeling the Multi-channel Section in the Supply Chain System using the Multiserver Queue Analogy

Murdapa

2021

jti

View full text Add to dashboard Cite

The industry generally consists of a supply chain system. The main constituents of any supply chain system are suppliers, manufacturers, distribution centers, and retailers. The system configuration can be straight chain, branched, cyclic, or a combination of all. An analytical model is needed to study system behavior as a result of the dynamics of its constituents. Modeling a multi-channel section becomes quite a challenging job in this regard. A method of modeling the multi-channel section will be discussed in this paper by adopting multi-server queues. As is well known, in a multi-server queue, there is a branching point at which the flow of entities begins to spread across several parallel servers. In the modeling perspective of this paper, the branching point is in the buffer (finished good warehouse in the factory, i.e., the focal echelon). That is the end of the waiting line from which the entity specifically moves to one of the servers, or in this context; it is called a channel. In this paper, the number of channels can be any, generalizable, can be more than two. Hence, the subsystem studied includes a factory, finished product warehouse, and several distribution centers. The factory produces by the mechanism of, where and r are stopping point and production restarting point, respectively. Production stops when the quantity of finished product in the warehouse reaches units and will restart the production when the quantity drops to the same or lower than units. The model is developed under Markovian assumptions by considering the quantities of production rates, the number of distribution centers (channels), travel time from factories to each distribution center, delivery lot size, and the time between the arrival of orders from distribution centers. The system under study is seen as a case of two echelons, namely factories and distribution channels. The numerical model obtained is applied to one case example with certain conditions. Comparisons with discrete simulation results give relatively small and acceptable differences. So, in the future, this model can complement the overall modeling of the supply chain system, a multi-echelon system with multi-channel distribution.

show abstract

Section: Modelingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modeling the Multi-channel Section in the Supply Chain System using the Multiserver Queue Analogy

Murdapa

2021

jti

View full text Add to dashboard Cite

show abstract

“…We note that in contrast to the classical models now the explicit formulas contain the continued fractions as components. For π ij (N ), (i, j) ∈ S(Q 1 , N) Kolmogorov equations can be solved in an explicit vector-matrix form (see [6]). The obtained results can be used to solve optimization problems in the class of threshold strategies (see, for example, [2][3][4][5]10]).…”

Section: The Expression From (5)mentioning

confidence: 99%

On Multiserver State-Dependent Retrial Queues Operating in Stationary Regime

Lebedev

Ponomarov

Pryshchepa

2021

Information Technologies and Mathematical Modelling. Queueing Theory and Applications

View full text Add to dashboard Cite

In this paper, we consider Markov models for two types of multiserver retrial queues with an input flow rate that depends on a number of calls in an orbit: classical state-dependent models and statedependent queues with limited number of retrials. For both systems, the conditions for the existence of the stationary regime are defined and formulas for steady-state probabilities are presented. The investigative technique is based on approximation of the input system by the system with truncated state space.

show abstract

“…From a practical point of view, systems with variable input flow are very important and have to be tackled. The input flow rate in these systems depends on the number of repeated calls in the current moment of time [2]. This allows control of the input flow for maximizing the quality of service and maximizing the income from the system.…”

Section: Introductionmentioning

confidence: 99%

On Stationary Probabilities of State-Dependent Markov Retrial Queue

Pryshchepa

2023

MCIT

View full text Add to dashboard Cite

In this paper, we consider the Markov model of a multiserver retrial queue with an input flow rate that depends on the number of calls in an orbit and with a limited number of retrials. We have obtained the conditions for the existence of the stationary regime and presented formulas for steady-state probabilities. Our approach is based on the approximation of the input model by the model with truncated state space.

show abstract

On a Multi-Channel Retrial Queueing System

Cited by 3 publications

References 3 publications

Modeling the Multi-channel Section in the Supply Chain System using the Multiserver Queue Analogy

Modeling the Multi-channel Section in the Supply Chain System using the Multiserver Queue Analogy

On Multiserver State-Dependent Retrial Queues Operating in Stationary Regime

On Stationary Probabilities of State-Dependent Markov Retrial Queue

Contact Info

Product

Resources

About