scholarly journals A detailed note on the finite-buffer queueing system with correlated batch-arrivals and batch-size-/phase-dependent bulk-service

4OR ◽  
2021 ◽  
Author(s):  
Souvik Ghosh ◽  
A. D. Banik ◽  
Joris Walraevens ◽  
Herwig Bruneel
Keyword(s):  
Queueing System ◽  
Batch Size ◽  
Finite Buffer ◽  
Batch Arrivals ◽  
Bulk Service

scholarly journals Transient and Stationary Losses in a Finite-Buffer Queue with Batch Arrivals

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Andrzej Chydzinski ◽  
Blazej Adamczyk
Keyword(s):  
Batch Size ◽  
Buffer Size ◽  
Arrival Process ◽  
Time Interval ◽  
Finite Buffer ◽  
Finite Time Interval ◽  
Batch Arrivals ◽  
Batch Markovian Arrival Process ◽  
Buffer Overflows ◽  
Finite Buffer Queue

We present an analysis of the number of losses, caused by the buffer overflows, in a finite-buffer queue with batch arrivals and autocorrelated interarrival times. Using the batch Markovian arrival process, the formulas for the average number of losses in a finite time interval and the stationary loss ratio are shown. In addition, several numerical examples are presented, including illustrations of the dependence of the number of losses on the average batch size, buffer size, system load, autocorrelation structure, and time.

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.

On infinite server queues with batch arrivals

1966 ◽  
Vol 3 (1) ◽  
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 ar(r ≧ 1),(vi)the batch sizes, the service times and the arrivals are independent.

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