The waiting time distribution for a correlated queue with exponential interarrival and service times

2018 ◽  
Vol 46 (2) ◽  
pp. 268-271 ◽  
Author(s):  
Bara Kim ◽  
Jeongsim Kim
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Waiting Time Distribution ◽  
Service Times

scholarly journals The Waiting-Time Distribution for the GI/G/1 Queue under the D-Policy

1992 ◽  
Vol 6 (3) ◽  
pp. 287-308 ◽  
Author(s):  
Jingwen Li ◽  
Shun-Chen Niu
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Busy Period ◽  
Waiting Times ◽  
Optimization Models ◽  
Arrival Process ◽  
Waiting Time Distribution ◽  
Service Times

We study a generalization of the GI/G/l queue in which the server is turned off at the end of each busy period and is reactivated only when the sum of the service times of all waiting customers exceeds a given threshold of size D. Using the concept of a “randomly selected” arriving customer, we obtain as our main result a relation that expresses the waiting-time distribution of customers in this model in terms of characteristics associated with a corresponding standard GI/G/1 queue, obtained by setting D = 0. If either the arrival process is Poisson or the service times are exponentially distributed, then this representation of the waiting-time distribution can be specialized to yield explicit, transform-free formulas; we also derive, in both of these cases, the expected customer waiting times. Our results are potentially useful, for example, for studying optimization models in which the threshold D can be controlled.

The waiting-time process of a queueing system with gamma-type input and blocking

1986 ◽  
Vol 23 (01) ◽  
pp. 166-174 ◽  
Author(s):  
C. Langaris
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Queueing System ◽  
Queueing Network ◽  
Time Process ◽  
Waiting Time Distribution ◽  
Second Stage ◽  
The Laplace Transform ◽  
Waiting Time Process ◽  
Service Times

In this work the first-come-first-served waiting-time process of a customer in a two-stage queueing network without intermediate waiting space is analysed. We assume that the arrivals follow the gamma distribution, the service times in the first stage are arbitrarily distributed, and the service times in the second stage are again of gamma type. Connecting the waiting time of the (n + 1)th customer with that of the nth and locating the zeros of a certain function we derive expressions for the Laplace transform of the waiting-time distribution both in the transient and the steady state.

The waiting-time process of a queueing system with gamma-type input and blocking

1986 ◽  
Vol 23 (1) ◽  
pp. 166-174 ◽  
Author(s):  
C. Langaris
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Queueing System ◽  
Queueing Network ◽  
Time Process ◽  
Waiting Time Distribution ◽  
Second Stage ◽  
The Laplace Transform ◽  
Waiting Time Process ◽  
Service Times

In this work the first-come-first-served waiting-time process of a customer in a two-stage queueing network without intermediate waiting space is analysed. We assume that the arrivals follow the gamma distribution, the service times in the first stage are arbitrarily distributed, and the service times in the second stage are again of gamma type.Connecting the waiting time of the (n + 1)th customer with that of the nth and locating the zeros of a certain function we derive expressions for the Laplace transform of the waiting-time distribution both in the transient and the steady state.

Some analyses on the control of queues using level crossings of regenerative processes

1980 ◽  
Vol 17 (3) ◽  
pp. 814-821 ◽  
Author(s):  
J. G. Shanthikumar
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Queueing Systems ◽  
Density Functions ◽  
Waiting Time Distribution ◽  
Regenerative Processes ◽  
Stieltjes Transform ◽  
Expected Number ◽  
Control Of Queues ◽  
Special Case

Some properties of the number of up- and downcrossings over level u, in a special case of regenerative processes are discussed. Two basic relations between the density functions and the expected number of upcrossings of this process are derived. Using these reults, two examples of controlled M/G/1 queueing systems are solved. Simple relations are derived for the waiting time distribution conditioned on the phase of control encountered by an arriving customer. The Laplace-Stieltjes transform of the distribution function of the waiting time of an arbitrary customer is also derived for each of these two examples.

scholarly journals Role of the Solar Minimum in the Waiting Time Distribution Throughout the Heliosphere

2021 ◽  
Author(s):  
Yosia I Nurhan ◽  
Jay Robert Johnson ◽  
Jonathan R Homan ◽  
Simon Wing
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Solar Minimum ◽  
Waiting Time Distribution

CONTINUOUS-TIME FINANCE AND THE WAITING TIME DISTRIBUTION: MULTIPLE CHARACTERISTIC TIMES

2012 ◽  
Vol 26 (23) ◽  
pp. 1250151 ◽  
Author(s):  
KWOK SAU FA
Keyword(s):  
Distribution Function ◽  
Random Walk ◽  
Waiting Time ◽  
Continuous Time ◽  
Probability Distribution Function ◽  
Time Distribution ◽  
Waiting Time Distribution ◽  
Exponential Functions ◽  
Multiple Characteristic ◽  
Sum Of Products

In this paper, we model the tick-by-tick dynamics of markets by using the continuous-time random walk (CTRW) model. We employ a sum of products of power law and stretched exponential functions for the waiting time probability distribution function; this function can fit well the waiting time distribution for BUND futures traded at LIFFE in 1997.

Part Waiting Time Distribution in a Two-Machine Line

2012 ◽  
Vol 45 (6) ◽  
pp. 457-462 ◽  
Author(s):  
Chuan Shi ◽  
Stanley B. Gershwin
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Waiting Time Distribution
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