Time dependent solution of two stages M[X]/G/1 queue model server vacation random setup time and balking with Bernoulli schedule

2020 ◽  
Author(s):  
S. Shyamala ◽  
R. Vijayaraj
Keyword(s):  
Setup Time ◽  
Time Dependent ◽  
Server Vacation ◽  
Queue Model ◽  
Two Stages ◽  
Time Dependent Solution ◽  
Bernoulli Schedule

A note on the time-dependent and the stationary behaviour of a semi-infinite reservoir subject to a combination of Markovian inflows

1971 ◽  
Vol 8 (04) ◽  
pp. 708-715 ◽  
Author(s):  
Emlyn H. Lloyd
Keyword(s):  
Functional Equation ◽  
Explicit Formula ◽  
Generating Function ◽  
Present Theory ◽  
The Other ◽  
Time Dependent ◽  
Independent Sequence ◽  
Time Dependent Solution ◽  
Infinite Reservoir ◽  
Stationary Behaviour

The present theory of finite reservoirs is not rich in general theorems even when of the simple Moran type, with unit draft and stationary discrete independent-sequence inflows. For the corresponding systems with unbounded capacity however there are two classes of results which have been known for some time. One of these classes is concerned with the time-dependent solution, where the theory provides a functional equation for the generating function of the time to first emptiness (Kendall (1957)), and the other with the asymptotic stationary distribution of reservoir contents, for which an explicit formula for the generating function is available (Moran (1959)).

Hybrid heuristic time dependent solution of the radiative transfer equation for the slab

2009 ◽  
Author(s):  
Fabrizio Martelli ◽  
Samuele Del Bianco ◽  
Antonio Pifferi ◽  
Lorenzo Spinelli ◽  
Alessandro Torricelli ◽  
...  
Keyword(s):  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Time Dependent ◽  
Hybrid Heuristic ◽  
Time Dependent Solution

Time-dependent process of M/G/1 vacation models with exhaustive service

1992 ◽  
Vol 29 (02) ◽  
pp. 418-429 ◽  
Author(s):  
Hideaki Takagi
Keyword(s):  
Steady State ◽  
Initial Conditions ◽  
Setup Time ◽  
Time Dependent ◽  
Time Model ◽  
Vacation Models ◽  
Single Vacation ◽  
Multiple Vacation ◽  
Virtual Waiting Time ◽  
Vacation Model

Generalized M/G/1 vacation systems with exhaustive service include multiple and single vacation models and a setup time model possibly combined with an N-policy. In these models with given initial conditions, the time-dependent joint distribution of the server's state, the queue size, and the remaining vacation or service time is known (Takagi (1990)). In this paper, capitalizing on the above results, we obtain the Laplace transforms (with respect to time) for the distributions of the virtual waiting time, the unfinished work (backlog), and the depletion time. The steady-state limits of those transforms are also derived. An erroneous expression for the steady-state distribution of the depletion time in a multiple vacation model given by Keilson and Ramaswamy (1988) is corrected.

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