Analysis of dual tandem queues with a finite buffer capacity and non-overlapping service times and subject to breakdowns

2015 ◽  
Vol 47 (12) ◽  
pp. 1329-1341 ◽  
Author(s):  
Kan Wu ◽  
Ning Zhao
Keyword(s):  
Buffer Capacity ◽  
Finite Buffer ◽  
Tandem Queues ◽  
Service Times

Analysis of tandem queues with finite buffer capacity

2017 ◽  
Vol 49 (11) ◽  
pp. 1001-1013 ◽  
Author(s):  
Kan Wu ◽  
Yichi Shen ◽  
Ning Zhao
Keyword(s):  
Buffer Capacity ◽  
Finite Buffer ◽  
Tandem Queues

The dependence of sojourn times on service times in tandem queues

1984 ◽  
Vol 21 (3) ◽  
pp. 661-667 ◽  
Author(s):  
Xi-Ren Cao
Keyword(s):  
Sojourn Time ◽  
Past History ◽  
Interarrival Time ◽  
Conditional Probabilities ◽  
Tandem Queues ◽  
Sojourn Times ◽  
Distributed Service ◽  
Service Times

In this paper we study a series of servers with exponentially distributed service times. We find that the sojourn time of a customer at any server depends on the customer's past history only through the customer's interarrival time to that server. A method of calculating the conditional probabilities of sojourn times is developed.

scholarly journals Homogeneous row-continuous bivariate markov chains with boundaries

1988 ◽  
Vol 25 (A) ◽  
pp. 237-256
Author(s):  
J. Keilson ◽  
M. Zachmann
Keyword(s):  
Data Transmission ◽  
Communication Systems ◽  
Buffer Capacity ◽  
Passage Time ◽  
Finite Buffer ◽  
Transition Rates ◽  
Boundary Problems ◽  
Ergodic Distribution ◽  
The Matrix ◽  
Voice Data

The matrix-geometric results of M. Neuts are extended to ergodic row-continuous bivariate Markov processes [J(t), N(t)] on state space B = {(j, n)} for which: (a) there is a boundary level N for N(t) associated with finite buffer capacity; (b) transition rates to adjacent rows and columns are independent of row level n in the interior of B. Such processes are of interest in the modelling of queue-length for voice-data transmission in communication systems. One finds that the ergodic distribution consists of two decaying components of matrix-geometric form, the second induced by the finite buffer capacity. The results are obtained via Green's function methods and compensation. Passage-time distributions for the two boundary problems are also made available algorithmically.

scholarly journals Volume and duration of losses in finite buffer fluid queues

2015 ◽  
Vol 52 (3) ◽  
pp. 826-840 ◽  
Author(s):  
Fabrice Guillemin ◽  
Bruno Sericola
Keyword(s):  
Busy Period ◽  
Buffer Capacity ◽  
Exact Expression ◽  
Loss Probability ◽  
Finite Buffer ◽  
Fluid Queues ◽  
Buffer Content ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Arrival Processes

We study congestion periods in a finite fluid buffer when the net input rate depends upon a recurrent Markov process; congestion occurs when the buffer content is equal to the buffer capacity. Similarly to O'Reilly and Palmowski (2013), we consider the duration of congestion periods as well as the associated volume of lost information. While these quantities are characterized by their Laplace transforms in that paper, we presently derive their distributions in a typical stationary busy period of the buffer. Our goal is to compute the exact expression of the loss probability in the system, which is usually approximated by the probability that the occupancy of the infinite buffer is greater than the buffer capacity under consideration. Moreover, by using general results of the theory of Markovian arrival processes, we show that the duration of congestion and the volume of lost information have phase-type distributions.

scholarly journals Stability of Switched Server Systems with Constraints on Service-Time and Capacity of Buffers

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Li Wang ◽  
Zhonghe He ◽  
Chi Zhang
Keyword(s):  
Periodic Orbit ◽  
Service Time ◽  
Buffer Capacity ◽  
Time Factors ◽  
Upper Bounds ◽  
Finite Buffer ◽  
Lower And Upper Bounds ◽  
Upper Limit ◽  
Server Systems ◽  
The Given

The execution of emptying policy ensures the convergence of any solution to the system to a unique periodic orbit, which does not impose constraints on service-time and capacity of buffers. Motivated by these problems, in this paper, the service-time-limited policy is first proposed based on the information resulted from the periodic orbit under emptying policy, which imposes lower and upper bounds on emptying time for the queue in each buffer, by introducing lower-limit and upper-limit service-time factors. Furthermore, the execution of service-time-limited policy in the case of finite buffer capacity is considered. Moreover, the notion of feasibility of states under service-time-limited policy is introduced and then the checking condition for feasibility of states is given; that is, the solution does not exceed the buffer capacity within the first cycle of the server. At last, a sufficient condition for determining upper-limit service-time factors ensuring that the given state is feasible is given.

scholarly journals On the independence of sojourn times in tandem queues

1989 ◽  
Vol 21 (2) ◽  
pp. 488-489 ◽  
Author(s):  
Thomas M. Chen
Keyword(s):  
Tandem Queues ◽  
Sojourn Times ◽  
Deterministic Service ◽  
Service Times

Reich (1957) proved that the sojourn times in two tandem queues are independent when the first queue is M/M /1 and the second has exponential service times. When service times in the first queue are not exponential, it has been generally expected that the sojourn times are not independent. A proof for the case of deterministic service times in the first queue is offered here.

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