Interdependent Queueing Model with Varying Bulk Service

2012 ◽  
Vol 2 (1) ◽  
pp. 109 ◽  
Author(s):  
T. S. R Murthy ◽  
Sivarama Krishna ◽  
G. V. S Raju
Keyword(s):  
Queueing Model ◽  
Bulk Service

scholarly journals Queues with two units connected in series with a multiserver bulk service with accessible and non accessible batch in unit II

2014 ◽  
Vol 4 (1) ◽  
Author(s):  
G. Ayyappan ◽  
S. Velmurugan
Keyword(s):  
Service Time ◽  
Subject Classification ◽  
Geometric Method ◽  
Finite Buffer ◽  
Queueing Model ◽  
Service Station ◽  
Matrix Geometric Method ◽  
In Series ◽  
Bulk Service ◽  
Number Of Customers

This paper analyses a queueing model consisting of two units I and II connected in series, separated by a finite buffer of size N. Unit I has only one exponential server capable of serving customers one at a time. Unit II consists of c parallel exponential servers and they serve customers in groups according to the bulk service rule. This rule admits each batch served to have not less than ‘a’ and not more than ‘b’ customers such that the arriving customers can enter service station without affecting the service time if the size of the batch being served is less than ‘d’ ( a ≤ d ≤ b ). The steady stateprobability vector of the number of customers waiting and receiving service in unit I and waiting in the buffer is obtained using the modified matrix-geometric method. Numerical results are also presented. AMS Subject Classification number: 60k25 and 65k30

scholarly journals Maximum Entropy Approach for Un-Reliable Server Vacation Queueing Model with Optional Bulk Service

2012 ◽  
Vol 23 (1) ◽  
pp. 89-113
Author(s):  
Madhu Jain, Madhu Jain,
Keyword(s):  
Maximum Entropy ◽  
Performance Measures ◽  
Probability Generating Function ◽  
Single Server ◽  
Queueing Model ◽  
Time Service ◽  
Server Vacation ◽  
Single Vacation ◽  
Bulk Service ◽  
Essential Service

In this study, we consider a single server vacation queueing model with optional bulk service and an un-reliable server. A single server provides first essential service (FES) to all arriving customers one by one; apart from essential service, he can also facilitate the additional phase of optional service (OS) in batches of fixed size b( ≥ 1), in case when the customers request for it. The server may take a single vacation whenever he finds no customers waiting in the queue to be served. Moreover, the server is subjected to unpredictable breakdown while providing the first essential service. The vacation time, service time and repair time of the server are exponentially distributed. The steady state results are obtained in terms of probability generating function for queue size distributions. By using the maximum entropy analysis (MEA), we derive various system performance measures. A comparative study is performed between the exact and approximate waiting time of the system. By taking the numerical illustrations, the sensitivity analysis is done to explore the effect of different descriptors on various performance measures.

scholarly journals A Real-Time Chain and Variable Bulk Arrival and Variable Bulk Service (VBAVBS) Model with λF

2020 ◽  
Vol 10 (10) ◽  
pp. 3651
Author(s):  
Nohpill Park ◽  
Abhilash Kancharla ◽  
Hye-Young Kim
Keyword(s):  
Open Source ◽  
Real Time ◽  
Theoretical Foundation ◽  
Queueing Model ◽  
Time System ◽  
Real Time System ◽  
The Real ◽  
Proposed Model ◽  
Bulk Service ◽  
Bulk Arrival

This paper proposes a real-time chain and a novel embedded Markovian queueing model with variable bulk arrival (VBA) and variable bulk service (VBS) in order to establish and assure a theoretical foundation to design a blockchain-based real-time system with particular interest in Ethereum. Based on the proposed model, various performances are simulated in a numerical manner in order to validate the efficacy of the model by checking good agreements with the results against intuitive and typical expectations as a baseline. A demo of the proposed real-time chain is developed in this work by modifying the open source of Ethereum Geth 1.9.11. The work in this paper will provide both a theoretical foundation to design and optimize the performances of the proposed real-time chain, and ultimately address and resolve the performance bottleneck due to the conventional block-synchrony by employing an asynchrony by the real-time deadline to some extent.

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