Erlang loss queueing system with batch arrivals operating in a random environment

2009 ◽  
Vol 36 (3) ◽  
pp. 674-697 ◽  
Author(s):  
Che Soong Kim ◽  
Alexander Dudin ◽  
Valentina Klimenok ◽  
Valentina Khramova
Keyword(s):  
Random Environment ◽  
Queueing System ◽  
Batch Arrivals ◽  
Erlang Loss

A Single Server Retrial Queueing System with Two Types of Batch Arrivals

2016 ◽  
pp. 55-70
Author(s):  
Kalyanaraman Rathinasabapathy
Keyword(s):  
Queueing System ◽  
Numerical Study ◽  
Priority Queue ◽  
Single Server ◽  
Type I ◽  
Type Ii ◽  
Operating Characteristics ◽  
Batch Arrivals ◽  
Retrial Queueing System ◽  
Retrial Queueing

A retrial queueing system with two types of batch arrivals is considered. The arrivals are called type I and type II customers. The type I customers arrive in batches of size k with probability c_k and type II customers arrive in batches of size k with probability d_k. Service time distributions are identical independent distributions and are different for both type of customers. If the arriving customers are blocked due to server being busy, type I customers are queued in a priority queue of infinity capacity whereas type II customers entered into retrial group in order to seek service again after a random amount of time. For this model the joint distribution of the number of customers in the priority queue and in the retrial group in closed form is obtained. Some particular models and operating characteristics are obtained. A numerical study is also carried out.

scholarly journals A queueing system with moving average input process and batch arrivals

1965 ◽  
Vol 5 (4) ◽  
pp. 434-442 ◽  
Author(s):  
C. Pearce
Keyword(s):  
Queueing System ◽  
Moving Average ◽  
Limiting Distribution ◽  
Input Process ◽  
Batch Arrivals

In a recent paper by P. D. Finch and myself [1], the solution for the limiting distribution of a moving average queueing system was obtained. In this paper the system is generalised to the case of batch arrivals in batches of size ρ > 1.

The retrial queueing system operating in random environment

2007 ◽  
Vol 137 (12) ◽  
pp. 3904-3916 ◽  
Author(s):  
Che Soong Kim ◽  
Valentina Klimenok ◽  
Sang Cheon Lee ◽  
Alexander Dudin
Keyword(s):  
Random Environment ◽  
Queueing System ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
System Operating

On infinite server queues with batch arrivals

1966 ◽  
Vol 3 (01) ◽  
pp. 274-279 ◽  
Author(s):  
D. N. Shanbhag
Keyword(s):  
Queueing System ◽  
Batch Size ◽  
List Type ◽  
Type Number ◽  
Batch Arrivals ◽  
Batch Sizes ◽  
Infinite Server Queues ◽  
Service Times ◽  
The One ◽  
Independent And Identically Distributed

The queueing system studied in this paper is the one in which (i) there are an infinite number of servers, (ii) initially (at t = 0) all the servers are idle, (iii) one server serves only one customer at a time and the service times are independent and identically distributed with distribution function B(t) (t > 0) and mean β(< ∞), (iv) the arrivals are in batches such that a batch arrives during (t, t + δt) with probability λ(t)δt + o(δt) (λ(t) > 0) and no arrival takes place during (t, t + δt) with the probability 1 –λ(t)δt + o(δt), (v) the batch sizes are independent and identically distributed with mean α(< ∞), and the probability that a batch size equals r is given by a r(r ≧ 1), (vi) the batch sizes, the service times and the arrivals are independent.

scholarly journals Queueing system with passive servers

1996 ◽  
Vol 9 (2) ◽  
pp. 185-204 ◽  
Author(s):  
Alexander N. Dudin ◽  
Valentina I. Klimenok
Keyword(s):  
Functional Equation ◽  
Markov Chain ◽  
Response Time ◽  
Stationary Distribution ◽  
Random Environment ◽  
Queueing System ◽  
Sufficient Conditions ◽  
Special Kind ◽  
Embedded Markov Chain ◽  
Matrix Analog

In this paper the authors introduce systems in which customers are served by one active server and a group of passive servers. The calculation of response time for such systems is rendered by analyzing a special kind of queueing system in a synchronized random environment. For an embedded Markov chain, sufficient conditions for the existence of a stationary distribution are proved. A formula for the corresponding vector generating function is obtained. It is a matrix analog of the Pollaczek-Khinchin formula and is simultaneously a matrix functional equation. A method for solving this equation is proposed.

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