Analysis of Closed Unreliable Queueing Networks with Batch Service

2021 ◽  
pp. 352-362
Author(s):  
Elena Stankevich ◽  
Igor Tananko ◽  
Oleg Osipov
Keyword(s):  
Queueing Networks ◽  
Batch Service

A stochastic lower bound for assemble-transfer batch service queueing networks

2000 ◽  
Vol 37 (3) ◽  
pp. 881-889 ◽  
Author(s):  
Antonis Economou
Keyword(s):  
Lower Bound ◽  
Stationary Distribution ◽  
Upper Bound ◽  
Queueing Networks ◽  
Product Form ◽  
Arrival Process ◽  
Batch Service ◽  
Original Network ◽  
Departure Process ◽  
Geometric Product

Miyazawa and Taylor (1997) introduced a class of assemble-transfer batch service queueing networks which do not have tractable stationary distribution. However by assuming a certain additional arrival process at each node when it is empty, they obtain a geometric product-form stationary distribution which is a stochastic upper bound for the stationary distribution of the original network. In this paper we develop a stochastic lower bound for the original network by introducing an additional departure process at each node which tends to remove all the customers present in it. This model in combination with the aforementioned upper bound model gives a better sense for the properties of the original network.

A stochastic lower bound for assemble-transfer batch service queueing networks

2000 ◽  
Vol 37 (03) ◽  
pp. 881-889 ◽  
Author(s):  
Antonis Economou
Keyword(s):  
Lower Bound ◽  
Stationary Distribution ◽  
Upper Bound ◽  
Queueing Networks ◽  
Product Form ◽  
Arrival Process ◽  
Batch Service ◽  
Original Network ◽  
Departure Process ◽  
Geometric Product

Miyazawa and Taylor (1997) introduced a class of assemble-transfer batch service queueing networks which do not have tractable stationary distribution. However by assuming a certain additional arrival process at each node when it is empty, they obtain a geometric product-form stationary distribution which is a stochastic upper bound for the stationary distribution of the original network. In this paper we develop a stochastic lower bound for the original network by introducing an additional departure process at each node which tends to remove all the customers present in it. This model in combination with the aforementioned upper bound model gives a better sense for the properties of the original network.

On the stochastic domination for batch-arrival, batch-service and assemble-transfer queueing networks

2003 ◽  
Vol 40 (04) ◽  
pp. 1103-1120 ◽  
Author(s):  
Antonis Economou
Keyword(s):  
Continuous Time ◽  
Queueing Networks ◽  
Stochastic Order ◽  
Batch Arrival ◽  
Batch Service ◽  
Stochastic Monotonicity ◽  
Stochastic Domination ◽  
Jackson Networks ◽  
Continuous Time Markov Chains

Stochastic monotonicity properties for various classes of queueing networks have been established in the literature mainly with the use of coupling constructions. Miyazawa and Taylor (1997) introduced a class of batch-arrival, batch-service and assemble-transfer queueing networks which can be thought of as generalized Jackson networks with batch movements. We study conditions for stochastic domination within this class of networks. The proofs are based on a certain characterization of the stochastic order for continuous-time Markov chains, written in terms of their associated intensity matrices.

ON TRUNCATION PROPERTIES OF FINITE-BUFFER QUEUES AND QUEUEING NETWORKS

2000 ◽  
Vol 14 (4) ◽  
pp. 409-423 ◽  
Author(s):  
Xiuli Chao ◽  
Masakiyo Miyazawa
Keyword(s):  
Stochastic Process ◽  
Continuous Time ◽  
Queueing Networks ◽  
Additional Condition ◽  
Queueing Systems ◽  
Batch Service ◽  
Single Server ◽  
Finite Buffer ◽  
Finite Buffers ◽  
Batch Service Queues

We show that several truncation properties of queueing systems are consequences of a simple property of censored stochastic processes. We first consider a discrete-time stochastic process and show that its censored process has a truncated stationary distribution. When the stochastic process has continuous time, we present a similar result under the additional condition that the process is locally balanced. We apply these results to single-server batch arrival batch service queues with finite buffers and queueing networks with finite buffers and batch movements, and extend the well-known results on truncation properties of the MX/G/1/k queues and queueing networks with jump-over blocking.

Queueing networks with batch service

2011 ◽  
Vol 5 (3) ◽  
pp. 313 ◽  
Author(s):  
Th. Hanschke ◽  
H. Zisgen
Keyword(s):  
Queueing Networks ◽  
Batch Service

scholarly journals Analysis of Closed Queueing Networks with Batch Service

2020 ◽  
Vol 20 (4) ◽  
pp. 527-533
Author(s):  
Elena P. Stankevich ◽  
◽  
Igor E. Tananko ◽  
Vitalii I. Dolgov ◽  
◽  
...  
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Queueing Networks ◽  
Manufacturing Systems ◽  
Queueing Network ◽  
Transport Systems ◽  
Batch Service ◽  
Single Server ◽  
Closed Queueing Networks ◽  
Number Of Customers

We consider a closed queuing network with batch service and movements of customers in continuous time. Each node in the queueing network is an infinite capacity single server queueing system under a RANDOM discipline. Customers move among the nodes following a routing matrix. Customers are served in batches of a fixed size. If a number of customers in a node is less than the size, the server of the system is idle until the required number of customers arrive at the node. An arriving at a node customer is placed in the queue if the server is busy. The batсh service time is exponentially distributed. After a batсh finishes its execution at a node, each customer of the batch, regardless of other customers of the batch, immediately moves to another node in accordance with the routing probability. This article presents an analysis of the queueing network using a Markov chain with continuous time. The qenerator matrix is constructed for the underlying Markov chain. We obtain expressions for the performance measures. Some numerical examples are provided. The results can be used for the performance analysis manufacturing systems, passenger and freight transport systems, as well as information and computing systems with parallel processing and transmission of information.

On the stochastic domination for batch-arrival, batch-service and assemble-transfer queueing networks

2003 ◽  
Vol 40 (4) ◽  
pp. 1103-1120 ◽  
Author(s):  
Antonis Economou
Keyword(s):  
Continuous Time ◽  
Queueing Networks ◽  
Stochastic Order ◽  
Batch Arrival ◽  
Batch Service ◽  
Stochastic Monotonicity ◽  
Stochastic Domination ◽  
Jackson Networks ◽  
Continuous Time Markov Chains

Stochastic monotonicity properties for various classes of queueing networks have been established in the literature mainly with the use of coupling constructions. Miyazawa and Taylor (1997) introduced a class of batch-arrival, batch-service and assemble-transfer queueing networks which can be thought of as generalized Jackson networks with batch movements. We study conditions for stochastic domination within this class of networks. The proofs are based on a certain characterization of the stochastic order for continuous-time Markov chains, written in terms of their associated intensity matrices.

Partial balances in batch arrival batch service and assemble-transfer queueing networks

1997 ◽  
Vol 34 (3) ◽  
pp. 745-752 ◽  
Author(s):  
Xiuli Chao
Keyword(s):  
Queueing Networks ◽  
Form Solution ◽  
Product Form ◽  
Batch Arrival ◽  
Arrival Process ◽  
Batch Service ◽  
Balance Equations ◽  
Steady State Probability ◽  
Simple Product ◽  
Necessary And Sufficient

Recently Miyazawa and Taylor (1997) proposed a new class of queueing networks with batch arrival batch service and assemble-transfer features. In such networks customers arrive and are served in batches, and may change size when a batch transfers from one node to another. With the assumption of an additional arrival process at each node when it is empty, they obtain a simple product-form steady-state probability distribution, which is a (stochastic) upper bound for the original network. This paper shows that this class of network possesses a set of non-standard partial balance equations, and it is demonstrated that the condition of the additional arrival process introduced by Miyazawa and Taylor is there precisely to satisfy the partial balance equations, i.e. it is necessary and sufficient not only for having a product form solution, but also for the partial balance equations to hold.

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