Loss Probability for a Finite Buffer Multiplexer with the M/G/∞ Input Process

2005 ◽  
Vol 29 (3) ◽  
pp. 181-197 ◽  
Author(s):  
George C. Lin ◽  
Tatsuya Suda ◽  
Fumio Ishizaki
Keyword(s):  
Loss Probability ◽  
Finite Buffer ◽  
Input Process

Loss Probability of a Burst Arrival Finite Queue with Synchronized Service

1992 ◽  
Vol 6 (2) ◽  
pp. 201-216 ◽  
Author(s):  
Masakiyo Miyazawa
Keyword(s):  
Markov Chain ◽  
Loss Probability ◽  
Buffer Size ◽  
Embedded Markov Chain ◽  
Main Concern ◽  
Single Server ◽  
Finite Buffer ◽  
Single Server Queue ◽  
Server Queue ◽  
Computation Algorithm

We are concerned with a burst arrival single-server queue, where arrivals of cells in a burst are synchronized with a constant service time. The main concern is with the loss probability of cells for the queue with a finite buffer. We analyze an embedded Markov chain at departure instants of cells and get a kind of lumpability for its state space. Based on these results, this paper proposes a computation algorithm for its stationary distribution and the loss probability. Closed formulas are obtained for the first two moments of the numbers of cells and active bursts when the buffer size is infinite.

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.

Cell loss probability for M/G/1 and time-slotted queues

2000 ◽  
Vol 37 (04) ◽  
pp. 1149-1156
Author(s):  
David McDonald ◽  
François Théberge
Keyword(s):  
Continuous Time ◽  
Time Slot ◽  
Arrival Rate ◽  
Cell Loss ◽  
Loss Probability ◽  
Finite Buffer ◽  
Asymptotic Results ◽  
Overflow Probability ◽  
The Mean

It is common practice to approximate the cell loss probability (CLP) of cells entering a finite buffer by the overflow probability (OVFL) of a corresponding infinite buffer queue, since the CLP is typically harder to estimate. We obtain exact asymptotic results for CLP and OVFL for time-slotted queues where block arrivals in different time slots are i.i.d. and one cell is served per time slot. In this case the ratio of CLP to OVFL is asymptotically (1-ρ)/ρ, where ρ is the use or, equivalently, the mean arrival rate per time slot. Analogous asymptotic results are obtained for continuous time M/G/1 queues. In this case the ratio of CLP to OVFL is asymptotically 1-ρ.

The Loss Probability in Finite-Buffer Queues with Batch Arrivals and Complete Rejection

1994 ◽  
Vol 8 (2) ◽  
pp. 221-227 ◽  
Author(s):  
Frank N. Gouweleeuw
Keyword(s):  
Loss Probability ◽  
Batch Arrival ◽  
Finite Buffer ◽  
Batch Arrivals ◽  
Complete Rejection

This note extends a recently proposed approximation for the loss probability to the batch-arrival Finite-buffer queues with complete rejection. Also, a condition is stated under which the approximation is exact.

scholarly journals COUNTEREXAMPLES TO A CONJECTURE ON BOUNDS FOR THE LOSS PROBABILITY IN FINITE-BUFFER QUEUES

1999 ◽  
Vol 13 (2) ◽  
pp. 221-227 ◽  
Author(s):  
Yiqiang Q. Zhao
Keyword(s):  
Lower Bounds ◽  
Loss Probability ◽  
Upper And Lower Bounds ◽  
Finite Buffer

In this paper, we provide counterexamples to a conjecture, made by Miyazawa and Tijms (1993), on the upper and lower bounds for the loss probability in finite-buffer queues.

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

2015 ◽  
Vol 52 (03) ◽  
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 Comparison of Two Approximations for the Loss Probability in Finite-Buffer Queues

1993 ◽  
Vol 7 (1) ◽  
pp. 19-27 ◽  
Author(s):  
Masakiyo Miyazawa ◽  
Henk Tijms
Keyword(s):  
Experimental Study ◽  
Lower Bounds ◽  
Empirical Finding ◽  
Practical Interest ◽  
Loss Probability ◽  
Upper And Lower Bounds ◽  
Finite Buffer ◽  
Theoretical Support

This paper deals with two related approximations that were recently proposed for the loss probability in finite-buffer queues. The purpose of the paper is twofold: first, to provide better insight and more theoretical support for both approximations, and second, to show by an experimental study how well both approximations perform. An interesting empirical finding is that in many cases of practical interest the two approximations provide upper and lower bounds on the exact value of the loss probability.

The analysis of a discrete time finite-buffer queue with working vacations under Markovian arrival process and PH-service time

2020 ◽  
Vol 54 (3) ◽  
pp. 675-691
Author(s):  
Qingqing Ye ◽  
Liwei Liu ◽  
Tao Jiang ◽  
Baoxian Chang
Keyword(s):  
Performance Measures ◽  
Discrete Time ◽  
Loss Probability ◽  
Combination Method ◽  
Arrival Process ◽  
Finite Buffer ◽  
The Matrix ◽  
Working Vacations ◽  
The Impact ◽  
Number Of Customers

In this paper, we study the discrete-time MAP/PH/1 queue with multiple working vacations and finite buffer N. Using the Matrix-Geometric Combination method, we obtain the stationary probability vectors of this model, which can be expressed as a linear combination of two matrix-geometric vectors. Furthermore, we obtain some performance measures including the loss probability and give the limit of loss probability as finite buffer N goes to infinite. Waiting time distribution is derived by using the absorbing Markov chain. Moreover, we obtain the number of customers served in the busy period. At last, some numerical examples are presented to verify the results we obtained and show the impact of parameter N on performance measures.

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