scholarly journals On finite capacity queues with time dependent arrival rates

2013 ◽  
Vol 123 (6) ◽  
pp. 2175-2227 ◽  
Author(s):  
Xiaoqian Tan ◽  
Charles Knessl ◽  
Yongzhi (Peter) Yang
Keyword(s):  
Time Dependent ◽  
Finite Capacity ◽  
Finite Capacity Queues

Scale functions of Lévy processes and busy periods of finite-capacity M/GI/1 queues

2004 ◽  
Vol 41 (4) ◽  
pp. 1145-1156 ◽  
Author(s):  
Parijat Dube ◽  
Fabrice Guillemin ◽  
Ravi R. Mazumdar
Keyword(s):  
Closed Form ◽  
Lévy Processes ◽  
Busy Period ◽  
Exit Time ◽  
Levy Processes ◽  
Finite Capacity ◽  
Scale Functions ◽  
Period Distribution ◽  
Finite Capacity Queues ◽  
Time Theory

In this paper we use the exit time theory for Lévy processes to derive new closed-form results for the busy period distribution of finite-capacity fluid M/G/1 queues. Based on this result, we then obtain the busy period distribution for finite-capacity queues with on–off inputs when the off times are exponentially distributed.

Scale functions of Lévy processes and busy periods of finite-capacity M/GI/1 queues

2004 ◽  
Vol 41 (04) ◽  
pp. 1145-1156 ◽  
Author(s):  
Parijat Dube ◽  
Fabrice Guillemin ◽  
Ravi R. Mazumdar
Keyword(s):  
Closed Form ◽  
Lévy Processes ◽  
Busy Period ◽  
Exit Time ◽  
Levy Processes ◽  
Finite Capacity ◽  
Scale Functions ◽  
Period Distribution ◽  
Finite Capacity Queues ◽  
Time Theory

In this paper we use the exit time theory for Lévy processes to derive new closed-form results for the busy period distribution of finite-capacity fluid M/G/1 queues. Based on this result, we then obtain the busy period distribution for finite-capacity queues with on–off inputs when the off times are exponentially distributed.

Analysis of finite-capacity polling systems

1991 ◽  
Vol 23 (2) ◽  
pp. 373-387 ◽  
Author(s):  
Hideaki Takagi
Keyword(s):  
Time Distribution ◽  
Arrival Process ◽  
Polling Systems ◽  
Single Server ◽  
Service Time Distribution ◽  
Finite Capacity ◽  
Poisson Arrival ◽  
Finite Capacity Queues ◽  
General Service ◽  
Limited Service

We consider a system of N finite-capacity queues attended by a single server in cyclic order. For each visit by the server to a queue, the service is given continuously until that queue becomes empty (exhaustive service), given continuously only to those customers present at the visiting instant (gated service), or given to only a single customer (limited service). The server then switches to the next queue with a random switchover time, and administers the same type of service there similarly. For such a system where each queue has a Poisson arrival process, general service time distribution, and finite capacity, we find the distribution of the waiting time at each queue by utilizing the known results for a single M/G/1/K queue with multiple vacations.

On a generalized finite-capacity storage model

1983 ◽  
Vol 20 (3) ◽  
pp. 663-674 ◽  
Author(s):  
Samuel W. Woolford
Keyword(s):  
Distribution Function ◽  
Markov Chain ◽  
State Space ◽  
Random Variables ◽  
Time Dependent ◽  
Finite Capacity ◽  
Random Input ◽  
Storage Model ◽  
Limit Distributions

This paper considers a finite-capacity storage model defined on a Markov chain {Xn; n = 0, 1, ·· ·}, having state space J ⊆ {1, 2, ·· ·}. If Xn = j, then there is a random ‘input' Vn(j) (a negative input implying a demand) of ‘type' j, having a distribution function Fj(·). We assume that {Vn(j)} is an i.i.d. sequence of random variables, taken to be independent of {Xn} and of {Vn (k)}, for k ≠ j. Here, the random variables Vn(j) represent instantaneous ‘inputs' of type j for our storage model. Within this framework, we establish certain limit distributions for the joint processes (Zn, Xn) and (Zn, Qn, Ln), where Zn (defined in (1.2)) is the level of storage at time n, Qn (defined in (1.3)) is the cumulative overflow at time n, and Ln (defined in (1.4)) is the cumulative demand lost due to shortage of supply up to time n. In addition, an expression for the time-dependent distribution of (Zn, Xn) is obtained.

Analysis of finite-capacity polling systems

1991 ◽  
Vol 23 (02) ◽  
pp. 373-387 ◽  
Author(s):  
Hideaki Takagi
Keyword(s):  
Time Distribution ◽  
Arrival Process ◽  
Polling Systems ◽  
Single Server ◽  
Service Time Distribution ◽  
Finite Capacity ◽  
Poisson Arrival ◽  
Finite Capacity Queues ◽  
General Service ◽  
Limited Service

We consider a system of N finite-capacity queues attended by a single server in cyclic order. For each visit by the server to a queue, the service is given continuously until that queue becomes empty (exhaustive service), given continuously only to those customers present at the visiting instant (gated service), or given to only a single customer (limited service). The server then switches to the next queue with a random switchover time, and administers the same type of service there similarly. For such a system where each queue has a Poisson arrival process, general service time distribution, and finite capacity, we find the distribution of the waiting time at each queue by utilizing the known results for a single M/G/1/K queue with multiple vacations.

scholarly journals Modeling Curbside Parking as a Network of Finite Capacity Queues

2020 ◽  
Vol 21 (3) ◽  
pp. 1011-1022
Author(s):  
Chase P. Dowling ◽  
Lillian J. Ratliff ◽  
Baosen Zhang
Keyword(s):  
Finite Capacity ◽  
Finite Capacity Queues
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