scholarly journals Study on Transient Queue-Size Distribution in the Finite-Buffer Model with Batch Arrivals and Multiple Vacation Policy

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1410
Author(s):  
Wojciech M. Kempa ◽  
Rafał Marjasz
Keyword(s):  
Size Distribution ◽  
Algebraic Approach ◽  
Telecommunication Networks ◽  
Service Rate ◽  
Total Probability ◽  
Finite Buffer ◽  
Queue Size ◽  
Batch Arrivals ◽  
The Impact ◽  
Initial Buffer

The transient behavior of the finite-buffer queueing model with batch arrivals and generally distributed repeated vacations is analyzed. Such a system has potential applications in modeling the functioning of production systems, computer and telecommunication networks with energy saving mechanism based on cyclic monitoring the queue state (Internet of Things, wireless sensors networks, etc.). Identifying renewal moments in the evolution of the system and applying continuous total probability law, a system of Volterra-type integral equations for the time-dependent queue-size distribution, conditioned by the initial buffer state, is derived. A compact-form solution for the corresponding system written for Laplace transforms is obtained using an algebraic approach based on Korolyuk’s potential method. An illustrative numerical example presenting the impact of the service rate, arrival rate, initial buffer state and single vacation duration on the queue-size distribution is attached as well.

Analytical Solution for Time-Dependent Queue-Size Behavior in the Manufacturing Line with Finite Buffer Capacity and Machine Setup and Closedown Times

2015 ◽  
Vol 809-810 ◽  
pp. 1360-1365 ◽  
Author(s):  
Wojciech M. Kempa ◽  
Iwona Paprocka
Keyword(s):  
Buffer Capacity ◽  
Algebraic Approach ◽  
Markov Property ◽  
Setup Times ◽  
Total Probability ◽  
Finite Buffer ◽  
Queue Size ◽  
Continuous Version ◽  
Idle Period ◽  
Manufacturing Line

A single reliable-machine manufacturing line with finite buffer capacity is considered, in which each idle period is preceded by a random closedown time, and each busy period is preceded by a random setup time. The stream of arriving jobs is described by a simple Poisson process, while processing (service), closedown and setup times are generally distributed random variables. A system of Volterra-type integral equations for the transient queue-size distribution conditioned by the initial level of buffer saturation is found by using the Markov property of successive service completion epochs and the continuous version of total probability law. A parallel system written for Laplace transforms is obtained and written in a specific form. The solution of the latter system is derived in a compact-form applying the linear algebraic approach. The final representations are found in terms of “input” system parameters (transforms of processing, closedown and setup times’ distributions) and certain sequence defined recursively.

scholarly journals Simulation and Analysis of Impact of Buffering of Voice Calls in Integrated Voice and Data Communication System

2012 ◽  
pp. 112-116
Author(s):  
V M. Chavan ◽  
M M. Kuber ◽  
R J. Mukhedkar
Keyword(s):  
Communication System ◽  
Queuing Theory ◽  
Data Communication ◽  
Service Rate ◽  
Queue Size ◽  
Markov Chain Analysis ◽  
Chain Analysis ◽  
Voice Calls ◽  
The Impact ◽  
The Voice

Queuing theory and Markov chain analysis plays vital role in analyzing real-life problems. It is applied to wired network, wireless network and mobile communication to analyze the packet traffic in packet switched network. In this simulation and analysis, integrated communication system such as voice and data is simulated with different queue size for voice calls with different arrival and service rate and its results are analyzed to study the impact of buffering of voice and data calls for the proposed integrated wired network using Queuing theory and Markov chain analysis. We also propose to optimize the system characteristics in an attempt to provide better Quality of Service (QoS) for systems with integrated voice and data calls. The proposed models have two traffic flow namely voice calls (real-time traffic like audio) and data calls (data traffic like FTP). A single channel is assigned for voice and data calls. The incoming voice and data calls are queued when the channel is busy. Voice calls are delay-sensitive therefore priority is assigned to Constant Bit Rate (CBR) traffic voice request. For such systems, it is important to analyze the impact of buffering the voice calls as well as data calls for various mean arrival rates and mean service times for voice and data call requests. The impact of buffering the voice calls with different queue size, mean arrival rates and service rate are analyzed. These results of dedicated integrated voice and data communication system can be used for simulating any type of wired network. The minimum buffer or jitter required for both the traffic is calculated using Packet Delivery Fraction (PDF).

On Departure Process in a Production Model with Cyclic Working and Repair Periods

2014 ◽  
Vol 1036 ◽  
pp. 846-851 ◽  
Author(s):  
Wojciech M. Kempa ◽  
Iwona Paprocka ◽  
Krzysztof Kalinowski ◽  
Cezary Grabowik
Keyword(s):  
Probability Distributions ◽  
Algebraic Approach ◽  
Fixed Time ◽  
Form Solution ◽  
Repair Time ◽  
Production Model ◽  
Embedded Markov Chain ◽  
Total Probability ◽  
Finite Buffer ◽  
Departure Process

A finite-buffer queueing system of the M/M/1/N type is used for modeling the operation of a single-machine production line with cyclic failure-free and repair periods. The arriving jobs enter randomly according to a Poisson process and are being processed individually with service times having the common exponential distribution. After an exponentially distributed working period a breakdown of the machine occurs, starting an exponentially distributed repair time during which the service process is stopped. At the completion epoch of the repair time a new working period begins and so on. A system of integral equations for conditional probability distributions of the number of jobs completely processed before the fixed time t (departure process) is built, using the concept of embedded Markov chain and the total probability law. Applying linear-algebraic approach the compact-form solution of the corresponding system written for double transforms of departure process is found.

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