scholarly journals On time-dependent queue-size distribution in a model with finite buffer capacity and deterministic multiple vacations with applications to LTE DRX mechanism modeling

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Wojciech M. Kempa ◽  
Kamil Ksiazek ◽  
Rafal Marjasz
Keyword(s):  
Size Distribution ◽  
Buffer Capacity ◽  
Time Dependent ◽  
Finite Buffer ◽  
Queue Size ◽  
Multiple Vacations ◽  
Mechanism Modeling

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 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.

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