Analytic characterization of the optimal control of a queueing system

1970 ◽  
Vol 7 (03) ◽  
pp. 617-633 ◽  
Author(s):  
S. Zacks ◽  
M. Yadin
Keyword(s):  
Optimal Control ◽  
Queueing System ◽  
Control Policy ◽  
Random Variable ◽  
Management Policy ◽  
Homogeneous Poisson Process ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Arrival Intensity

Summary In a recent paper [7] the authors studied the optimal control policy of the following queueing system. Customers arrive at a service station according to a time homogeneous Poisson process with a known arrival intensity, λ. The service time at the station is a random variable having a negative exponential distribution with intensity μ, which is under control and can be varied over a certain range, according to the management policy.

Analytic characterization of the optimal control of a queueing system

1970 ◽  
Vol 7 (3) ◽  
pp. 617-633 ◽  
Author(s):  
S. Zacks ◽  
M. Yadin
Keyword(s):  
Optimal Control ◽  
Queueing System ◽  
Control Policy ◽  
Random Variable ◽  
Management Policy ◽  
Homogeneous Poisson Process ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Arrival Intensity

SummaryIn a recent paper [7] the authors studied the optimal control policy of the following queueing system. Customers arrive at a service station according to a time homogeneous Poisson process with a known arrival intensity, λ. The service time at the station is a random variable having a negative exponential distribution with intensity μ, which is under control and can be varied over a certain range, according to the management policy.

A characterization of the negative exponential distribution with application to reliability theory

1981 ◽  
Vol 18 (3) ◽  
pp. 652-659 ◽  
Author(s):  
M. J. Phillips
Keyword(s):  
Exponential Distribution ◽  
Random Variables ◽  
Reliability Theory ◽  
The Other ◽  
Independent Random Variables ◽  
System Availability ◽  
Failure Times ◽  
Negative Exponential Distribution ◽  
Negative Exponential

The negative exponential distribution is characterized in terms of two independent random variables. Only one of the random variables has a negative exponential distribution whilst the other can belong to a wide class of distributions. This result is then applied to two models for the reliability of a system of two modules subject to revealed and unrevealed faults to show when the models are equivalent. It is also shown, under certain conditions, that the system availability is only independent of the distribution of revealed failure times in one module when unrevealed failure times in the other module have a negative exponential distribution.

A characterization of the negative exponential distribution with application to reliability theory

1981 ◽  
Vol 18 (03) ◽  
pp. 652-659 ◽  
Author(s):  
M. J. Phillips
Keyword(s):  
Exponential Distribution ◽  
Random Variables ◽  
Reliability Theory ◽  
The Other ◽  
Independent Random Variables ◽  
System Availability ◽  
Failure Times ◽  
Negative Exponential Distribution ◽  
Negative Exponential

The negative exponential distribution is characterized in terms of two independent random variables. Only one of the random variables has a negative exponential distribution whilst the other can belong to a wide class of distributions. This result is then applied to two models for the reliability of a system of two modules subject to revealed and unrevealed faults to show when the models are equivalent. It is also shown, under certain conditions, that the system availability is only independent of the distribution of revealed failure times in one module when unrevealed failure times in the other module have a negative exponential distribution.

scholarly journals Asymptotic results for multiplexing subexponential on-off processes

1999 ◽  
Vol 31 (02) ◽  
pp. 394-421 ◽  
Author(s):  
Predrag R. Jelenković ◽  
Aurel A. Lazar
Keyword(s):  
Queueing System ◽  
Random Variable ◽  
Mean Value ◽  
Activity Period ◽  
Arrival Process ◽  
Asymptotic Results ◽  
Fluid Queue ◽  
Arrival Processes ◽  
Image Position

Consider an aggregate arrival process A N obtained by multiplexing N on-off processes with exponential off periods of rate λ and subexponential on periods τon. As N goes to infinity, with λN → Λ, A N approaches an M/G/∞ type process. Both for finite and infinite N, we obtain the asymptotic characterization of the arrival process activity period. Using these results we investigate a fluid queue with the limiting M/G/∞ arrival process A t ∞ and capacity c. When on periods are regularly varying (with non-integer exponent), we derive a precise asymptotic behavior of the queue length random variable Q t P observed at the beginning of the arrival process activity periods where ρ = 𝔼A t ∞ < c; r (c ≤ r) is the rate at which the fluid is arriving during an on period. The asymptotic (time average) queue distribution lower bound is obtained under more general assumptions regarding on periods than regular variation. In addition, we analyse a queueing system in which one on-off process, whose on period belongs to a subclass of subexponential distributions, is multiplexed with independent exponential processes with aggregate expected rate 𝔼e t . This system is shown to be asymptotically equivalent to the same queueing system with the exponential arrival processes being replaced by their total mean value 𝔼e t .

scholarly journals Gain from the two-envelope problem via information asymmetry: on the suboptimality of randomized switching

2011 ◽  
Vol 467 (2134) ◽  
pp. 2825-2851 ◽  
Author(s):  
Mark D. McDonnell ◽  
Alex J. Grant ◽  
Ingmar Land ◽  
Badri N. Vellambi ◽  
Derek Abbott ◽  
...  
Keyword(s):  
Information Asymmetry ◽  
Exponential Distribution ◽  
Random Variable ◽  
Mathematical Finance ◽  
Positive Random Variable ◽  
Optimal Switching ◽  
Switching Strategy ◽  
Negative Exponential Distribution ◽  
Negative Exponential

The two-envelope problem (or exchange problem) is one of maximizing the payoff in choosing between two values, given an observation of only one. This paradigm is of interest in a range of fields from engineering to mathematical finance, as it is now known that the payoff can be increased by exploiting a form of information asymmetry. Here, we consider a version of the ‘two-envelope game’ where the envelopes’ contents are governed by a continuous positive random variable. While the optimal switching strategy is known and deterministic once an envelope has been opened, it is not necessarily optimal when the content's distribution is unknown. A useful alternative in this case may be to use a switching strategy that depends randomly on the observed value in the opened envelope. This approach can lead to a gain when compared with never switching. Here, we quantify the gain owing to such conditional randomized switching when the random variable has a generalized negative exponential distribution, and compare this to the optimal switching strategy. We also show that a randomized strategy may be advantageous when the distribution of the envelope's contents is unknown, since it can always lead to a gain.

scholarly journals Profit Analysis of a Standby Repairable System with Priority to Preventive Maintenance and Rest of Server Between Repairs

2021 ◽  
Author(s):  
Chhama Aggarwal ◽  
Nitika Ahlawat ◽  
S.C. Malik
Keyword(s):  
Preventive Maintenance ◽  
Failure Time ◽  
Random Variable ◽  
Productivity Level ◽  
Reliability Characteristics ◽  
Profit Analysis ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
The Cost ◽  
Efficiency And Productivity

The paper aims to bring out the profit analysis of a system with cold standby redundancy of two identical units. In the system, we keep one unit productive and the other is to backup the operation. The system requires preventive maintenance after a specific time. In addition to that, the server is allowed to rest between two consecutive repairs. The repairs are done to increase the efficiency and productivity level of the system. The repair and rest times follow arbitrary distributions while the random variable related to failure time of the unit follows negative exponential distribution. The provision of priority has been made for the preventive maintenance over repairs. Some important reliability characteristics are studied in steady state by using the approach of stochastic processes. The revenue per unit time and the cost per unit time for which server is busy in repairs and maintenances are considered for determining the profit incurred to the system.  The results are shown graphically and numerically to highlight the effect of different parameters on some significant reliability characteristics.

scholarly journals Asymptotic results for multiplexing subexponential on-off processes

1999 ◽  
Vol 31 (2) ◽  
pp. 394-421 ◽  
Author(s):  
Predrag R. Jelenković ◽  
Aurel A. Lazar
Keyword(s):  
Queueing System ◽  
Random Variable ◽  
Mean Value ◽  
Activity Period ◽  
Arrival Process ◽  
Asymptotic Results ◽  
Fluid Queue ◽  
Arrival Processes ◽  
Image Position

Consider an aggregate arrival process AN obtained by multiplexing N on-off processes with exponential off periods of rate λ and subexponential on periods τon. As N goes to infinity, with λN → Λ, AN approaches an M/G/∞ type process. Both for finite and infinite N, we obtain the asymptotic characterization of the arrival process activity period.Using these results we investigate a fluid queue with the limiting M/G/∞ arrival process At∞ and capacity c. When on periods are regularly varying (with non-integer exponent), we derive a precise asymptotic behavior of the queue length random variable QtP observed at the beginning of the arrival process activity periods where ρ = 𝔼At∞ < c; r (c ≤ r) is the rate at which the fluid is arriving during an on period. The asymptotic (time average) queue distribution lower bound is obtained under more general assumptions regarding on periods than regular variation.In addition, we analyse a queueing system in which one on-off process, whose on period belongs to a subclass of subexponential distributions, is multiplexed with independent exponential processes with aggregate expected rate 𝔼et. This system is shown to be asymptotically equivalent to the same queueing system with the exponential arrival processes being replaced by their total mean value 𝔼et.

Sign in / Sign up

Export Citation Format

Share Document