On the input-output map of a G/G/1 queue

1994 ◽  
Vol 31 (4) ◽  
pp. 1128-1133 ◽  
Author(s):  
Cheng-Shang Chang
Keyword(s):  
Direct Consequence ◽  
Input Output ◽  
Input Process ◽  
Departure Process ◽  
Service Times ◽  
Interarrival Times ◽  
Independent And Identically Distributed

In this note, we consider G/G/1 queues with stationary and ergodic inputs. We show that if the service times are independent and identically distributed with unbounded supports, then for a given mean of interarrival times, the number of sequences (distributions) of interarrival times that induce identical distributions on interdeparture times is at most 1. As a direct consequence, among all the G/M/1 queues with stationary and ergodic inputs, the M/M/1 queue is the only queue whose departure process is identically distributed as the input process.

On the input-output map of a G/G/1 queue

1994 ◽  
Vol 31 (04) ◽  
pp. 1128-1133 ◽  
Author(s):  
Cheng-Shang Chang
Keyword(s):  
Direct Consequence ◽  
Input Output ◽  
Input Process ◽  
Departure Process ◽  
Service Times ◽  
Interarrival Times ◽  
Independent And Identically Distributed

In this note, we consider G/G/1 queues with stationary and ergodic inputs. We show that if the service times are independent and identically distributed with unbounded supports, then for a given mean of interarrival times, the number of sequences (distributions) of interarrival times that induce identical distributions on interdeparture times is at most 1. As a direct consequence, among all the G/M/1 queues with stationary and ergodic inputs, the M/M/1 queue is the only queue whose departure process is identically distributed as the input process.

Regeneration in tandem queues

1981 ◽  
Vol 13 (1) ◽  
pp. 221-230 ◽  
Author(s):  
E. Nummelin
Keyword(s):  
Markov Chain ◽  
Waiting Times ◽  
Tandem Queues ◽  
Tandem Queue ◽  
Input Process ◽  
Service Times ◽  
Interarrival Times ◽  
Regeneration Times

Consider a tandem queue with renewal input process and i.i.d. service times (at each server). This paper is concerned with the construction of regeneration times for the multivariate Markov chain formed by the interarrival times, waiting times and service times of the customers.

Regeneration in tandem queues

1981 ◽  
Vol 13 (01) ◽  
pp. 221-230 ◽  
Author(s):  
E. Nummelin
Keyword(s):  
Markov Chain ◽  
Waiting Times ◽  
Tandem Queues ◽  
Tandem Queue ◽  
Input Process ◽  
Service Times ◽  
Interarrival Times ◽  
Regeneration Times

Consider a tandem queue with renewal input process and i.i.d. service times (at each server). This paper is concerned with the construction of regeneration times for the multivariate Markov chain formed by the interarrival times, waiting times and service times of the customers.

An Uncertain Single-Server Queueing Model

2021 ◽  
pp. 2150001
Author(s):  
Kai Yao
Keyword(s):  
Queueing Theory ◽  
Busy Period ◽  
Queueing System ◽  
Single Server ◽  
Queueing Model ◽  
Uncertainty Distribution ◽  
Uncertain Variables ◽  
Service Efficiency ◽  
Service Times ◽  
Interarrival Times

In the queueing theory, the interarrival times between customers and the service times for customers are usually regarded as random variables. This paper considers human uncertainty in a queueing system, and proposes an uncertain queueing model in which the interarrival times and the service times are regarded as uncertain variables. The busyness index is derived analytically which indicates the service efficiency of a queueing system. Besides, the uncertainty distribution of the busy period is obtained.

Stochastic comparisons for fork-join queues with exponential processing times

1997 ◽  
Vol 34 (2) ◽  
pp. 487-497 ◽  
Author(s):  
Esther Frostig ◽  
Tapani Lehtonen
Keyword(s):  
Random Variables ◽  
Single Server ◽  
Departure Process ◽  
Stochastic Comparisons ◽  
Processing Times ◽  
Service Rates ◽  
Service Times ◽  
Stochastic Majorization

Consider a fork-join queue, where each job upon arrival splits into k tasks and each joins a separate queue that is attended by a single server. Service times are independent, exponentially distributed random variables. Server i works at rate , where μ is constant. We prove that the departure process becomes stochastically faster as the service rates become more homogeneous in the sense of stochastic majorization. Consequently, when all k servers work with equal rates the departure process is stochastically maximized.

Comparing multi-server queues with finite waiting rooms, I: Same number of servers

1979 ◽  
Vol 11 (2) ◽  
pp. 439-447 ◽  
Author(s):  
David Sonderman
Keyword(s):  
Queueing Systems ◽  
Stochastic Comparisons ◽  
Waiting Room ◽  
Service Times ◽  
Interarrival Times ◽  
Multi Server

We compare two queueing systems with the same number of servers that differ by having stochastically ordered service times and/or interarrival times as well as different waiting room capacities. We establish comparisons for the sequences of actual-arrival and departure epochs, and demonstrate by counterexample that many stochastic comparisons possible with infinite waiting rooms no longer hold with finite waiting rooms.

Input-Output Modeling and Control of the Departure Process of Busy Airports

2000 ◽  
Vol 8 (1) ◽  
pp. 1-32 ◽  
Author(s):  
Nicolas Pujet ◽  
Bertrand Delcaire ◽  
Eric Feron
Keyword(s):  
Input Output ◽  
Departure Process ◽  
Modeling And Control ◽  
And Control

ON THE DISCRETE-TIME G/GI/∞ QUEUE

2008 ◽  
Vol 22 (4) ◽  
pp. 557-585 ◽  
Author(s):  
Iddo Eliazar
Keyword(s):  
Fixed Points ◽  
Discrete Time ◽  
Generating Functions ◽  
Random Variables ◽  
Output Process ◽  
Input Output ◽  
Input Process ◽  
Probability Generating Functions ◽  
Queue Model ◽  
Multidimensional Probability

The discrete-time G/GI/∞ queue model is explored. Jobs arrive to an infinite-server queuing system following an arbitrary input process X; job sizes are general independent and identically distributed random variables. The system's output process Y (of job departures) and queue process N (tracking the number of jobs present in the system) are analyzed. Various statistics of the stochastic maps X↦ Y and X↦ N are explicitly obtained, including means, variances, autocovariances, cross-covariances, and multidimensional probability generating functions. In the case of stationary inputs, we further compute the spectral densities of the stochastic maps, characterize the fixed points (in the L2 sense) of the input–output map, precisely determine when the output and queue processes display either short-ranged or long-ranged temporal dependencies, and prove a decomposition result regarding the intrinsic L2 structure of general stationary G/GI/∞ systems.

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.

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