Analysis of a semi-open queueing network with Markovian arrival process

Kim, Jiseung; Dudin, Alexander; Dudin, Sergey; Kim, Che Soong

doi:10.1016/j.peva.2017.12.005

Cited by 13 publications

(19 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, the exact analysis even of the simplest network, with two exponential single-server nodes, Poisson arrival process, and an infinite queue, remains a difficult task [15]. The semi-open networks with external queue are mainly analyzed by approximate methods and the matrix-geometric method [19][20][21][22][23].…”

Section: Semi-open Network With Replacementmentioning

confidence: 99%

On Truncation of the Matrix-Geometric Stationary Distributions

2019

View full text Add to dashboard Cite

In this paper, we study queueing systems with an infinite and finite number of waiting places that can be modeled by a Quasi-Birth-and-Death process. We derive the conditions under which the stationary distribution for a loss system is a truncation of the stationary distribution of the Quasi-Birth-and-Death process and obtain the stationary distributions of both processes. We apply the obtained results to the analysis of a semi-open network in which a customer from an external queue replaces a customer leaving the system at the node from which the latter departed.

show abstract

Section: Semi-open Network With Replacementmentioning

confidence: 99%

On Truncation of the Matrix-Geometric Stationary Distributions

2019

View full text Add to dashboard Cite

show abstract

“…In our paper, we deal with a queuing network which belongs to a relatively new category of semi-open queuing networks that recently were applied for the analysis of various real-world systems. For the review of the state of the art and the references see, for example, References [5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

“…Semi-open queuing networks with MAP arrival process are analysed in References [7,10]. However, the retrial phenomenon is not taken into account in those papers.…”

mentioning

confidence: 99%

Analysis of a Semi-Open Queuing Network with a State Dependent Marked Markovian Arrival Process, Customers Retrials and Impatience

Kim

Dudin

et al. 2019

Mathematics

Self Cite

View full text Add to dashboard Cite

We consider a queuing network with single-server nodes and heterogeneous customers. The number of customers, which can obtain service simultaneously, is restricted. Customers that cannot be admitted to the network upon arrival make repeated attempts to obtain service. The service time at the nodes is exponentially distributed. After service completion at a node, the serviced customer can transit to another node or leave the network forever. The main features of the model are the mutual dependence of processes of customer arrivals and retrials and the impatience and non-persistence of customers. Dynamics of the network are described by a multidimensional Markov chain with infinite state space, state inhomogeneous behavior and special structure of the infinitesimal generator. The explicit form of the generator is derived. An effective algorithm for computing the stationary distribution of this chain is recommended. The expressions for computation of the key performance measures of the network are given. Numerical results illustrating the importance of the account of the mentioned features of the model are presented. The model can be useful for capacity planning, performance evaluation and optimization of various wireless telecommunication networks, transportation and manufacturing systems.

show abstract

“…Essential technical difficulty in analysis of such networks consists of the complexity of the multidimensional Markov chain describing the behavior of the network. We successfully overcome this difficulty only due to the recent experience in analysis of the semi-open queueing networks without the movement of the servers via the analysis of Markov chains with structured generator, see [12,13].…”

Section: Introductionmentioning

confidence: 99%

“…At the same time, the majority of the research is implemented under the assumption that the arrivals occur according to a stationary Poisson process that has a constant arrival rate. Quite a short list of papers dealing with queueing networks with Markovian arrival process (not relating with car sharing) can be found in recent papers by [12,14] and references therein. A possibility of transition of servers between the nodes is not considered in these papers.…”

Section: Introductionmentioning

confidence: 99%

Queueing Network with Moving Servers as a Model of Car Sharing Systems

2019

Self Cite

View full text Add to dashboard Cite

We consider a queueing network with a finite number of nodes and servers moving between the nodes as a model of car sharing. The arrival process of customers to various nodes is defined by a marked Markovian arrival process. The customer that arrives at a certain node when there is no idle server (car) is lost. Otherwise, he/she is able to start the service. With known probability, which depends on the node and the number of available cars, this customer can balk the service and leave the system. The service time of a customer has an exponential distribution. Location of the server in the network after service completion is random with the known probability distribution. The behaviour of the network is described by a multi-dimensional continuous-time Markov chain. The generator of this chain is derived which allows us to compute the stationary distribution of the network states. The formulas for computing the key performance indicators of the system are given. Numerical results are presented. They characterize the dependence of some performance measures of the network and the nodes on the total number of cars (fleet size of the car sharing system) and correlation in the arrival process.

show abstract

Analysis of a semi-open queueing network with Markovian arrival process

Cited by 13 publications

References 15 publications

On Truncation of the Matrix-Geometric Stationary Distributions

On Truncation of the Matrix-Geometric Stationary Distributions

Analysis of a Semi-Open Queuing Network with a State Dependent Marked Markovian Arrival Process, Customers Retrials and Impatience

Queueing Network with Moving Servers as a Model of Car Sharing Systems

Contact Info

Product

Resources

About