Distribution of the time to buffer overflow in the M/G/1/N-type queueing model with batch arrivals and multiple vacation policy

2019 ◽  
Vol 71 (3) ◽  
pp. 447-455 ◽  
Author(s):  
Wojciech M. Kempa ◽  
Rafał Marjasz
Keyword(s):  
Buffer Overflow ◽  
Queueing Model ◽  
Batch Arrivals ◽  
Multiple Vacation

On the Optimality of the Generalized Shortest Queue Policy

1990 ◽  
Vol 4 (4) ◽  
pp. 477-487 ◽  
Author(s):  
Arie Hordijk ◽  
Ger Koole
Keyword(s):  
Queueing Model ◽  
Finite Buffers ◽  
Batch Arrivals ◽  
Parallel Servers ◽  
Shortest Queue

Consider a queueing model in which arriving customers have to choose between m parallel servers, each with its own queue. We prove for general arrival streams that the policy which assigns to the shortest queue is stochastically optimal for models with finite buffers and batch arrivals.

scholarly journals Sample-Path Analysis of Single-Server Queue with Multiple Vacations

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Muhammad El-Taha
Keyword(s):  
Stochastic Process ◽  
Conservation Law ◽  
Sample Path ◽  
Single Server ◽  
Queueing Model ◽  
Single Server Queue ◽  
Sample Path Analysis ◽  
Multiple Vacation ◽  
Server Queue ◽  
Background Material

We a give deterministic (sample path) proof of a result that extends the Pollaczek-Khintchine formula for a multiple vacation single-server queueing model. We also give a conservation law for the same system with multiple classes. Our results are completely rigorous and hold under weaker assumptions than those given in the literature. We do not make stochastic assumptions, so the results hold almost surely on every sample path of the stochastic process that describes the system evolution. The article is self contained in that it gives a brief review of necessary background material.

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