A uniformly sharp monotonicity result for discrete fractional sequential differences

2017 ◽  
Vol 110 (2) ◽  
pp. 145-154 ◽  
Author(s):  
Christopher S. Goodrich
Keyword(s):  
Monotonicity Result

SINGLE-MACHINE MULTIPLE-RECIPE PREDICTIVE MAINTENANCE

2013 ◽  
Vol 27 (2) ◽  
pp. 209-235 ◽  
Author(s):  
Yiwei Cai ◽  
John J. Hasenbein ◽  
Erhan Kutanoglu ◽  
Melody Liao
Keyword(s):  
Optimal Policy ◽  
Predictive Maintenance ◽  
Production Costs ◽  
Threshold Policy ◽  
Discrete Time Markov Chain ◽  
System A ◽  
Long Run ◽  
Monotonicity Result ◽  
Maintenance Policies ◽  
Discounted Costs

This paper studies a multiple-recipe predictive maintenance problem with M/G/1 queueing effects. The server degrades according to a discrete-time Markov chain and we assume that the controller knows both the machine status and the current number of jobs in the system. The controller's objective is to minimize total discounted costs or long-run average costs which include preventative and corrective maintenance costs, holdings costs, and possibly production costs. An optimal policy determines both when to perform maintenance and which type of job to process. Since the policy takes into account the machine's degradation status, such control decisions are known as predictive maintenance policies. In the single-recipe case, we prove that the optimal policy is monotone in the machine status, but not in the number of jobs in the system. A similar monotonicity result holds in the two-recipe case. Finally, we provide computational results indicating that significant savings can be realized when implementing a predictive maintenance policies instead of a traditional job-based threshold policy for preventive maintenances.

Optimal control of service rates in networks of queues

1987 ◽  
Vol 19 (1) ◽  
pp. 202-218 ◽  
Author(s):  
Richard R. Weber ◽  
Shaler Stidham
Keyword(s):  
Rate Control ◽  
Queueing Networks ◽  
Arrival Rate ◽  
Service Rate ◽  
Discounted Cost ◽  
Holding Costs ◽  
Optimal Service ◽  
Monotonicity Result ◽  
Service Rates ◽  
Number Of Customers

We prove a monotonicity result for the problem of optimal service rate control in certain queueing networks. Consider, as an illustrative example, a number of ·/M/1 queues which are arranged in a cycle with some number of customers moving around the cycle. A holding cost hi(xi) is charged for each unit of time that queue i contains xi customers, with hi being convex. As a function of the queue lengths the service rate at each queue i is to be chosen in the interval , where cost ci(μ) is charged for each unit of time that the service rate μis in effect at queue i. It is shown that the policy which minimizes the expected total discounted cost has a monotone structure: namely, that by moving one customer from queue i to the following queue, the optimal service rate in queue i is not increased and the optimal service rates elsewhere are not decreased. We prove a similar result for problems of optimal arrival rate and service rate control in general queueing networks. The results are extended to an average-cost measure, and an example is included to show that in general the assumption of convex holding costs may not be relaxed. A further example shows that the optimal policy may not be monotone unless the choice of possible service rates at each queue includes 0.

A monotonicity result for discrete fractional difference operators

2014 ◽  
Vol 102 (3) ◽  
pp. 293-299 ◽  
Author(s):  
Rajendra Dahal ◽  
Christopher S. Goodrich
Keyword(s):  
Difference Operators ◽  
Fractional Difference ◽  
Monotonicity Result

A Monotonicity Result for Inspecting Independent Items

1989 ◽  
Vol 3 (1) ◽  
pp. 135-140
Author(s):  
F.K. Hwang ◽  
S.G. Papastavridis
Keyword(s):  
Cost Function ◽  
Failure Probability ◽  
General Model ◽  
Group Testing ◽  
Probabilistic Algorithms ◽  
Expected Number ◽  
Monotonicity Result ◽  
Crucial Part

Recently, the conjecture that the expected number of tests is nondecreasing in the failure probability for binomial group testing has been proved. The proof has also been extended to three models of multiaccess systems. However, probabilistic algorithms are used as a crucial part of these proofs. In this paper, we give conceptually simpler new proofs without using probabilistic algorithms. We also extend the result to a more general model where the number of tests is replaced by a cost function.

scholarly journals A monotonicity result for a G/GI/c queue with balking or reneging

2006 ◽  
Vol 43 (04) ◽  
pp. 1201-1205
Author(s):  
Serhan Ziya ◽  
Hayriye Ayhan ◽  
Robert D. Foley ◽  
Erol Peköz
Keyword(s):  
Loss System ◽  
Fixed Probability ◽  
Monotonicity Result

In a G/GI/c loss system with balking, reneging, or limited waiting space, deleting some of the arriving customers can either increase or decrease the fraction of the remaining arrivals who get served, depending on how customers are deleted. We present a model in which the random deletion of arrivals independently and with some fixed probability can never decrease the fraction of the remaining arrivals who get served.

A monotonicity result for a single-server queue subject to a Markov-modulated Poisson process

1995 ◽  
Vol 32 (4) ◽  
pp. 1103-1111 ◽  
Author(s):  
Qing Du
Keyword(s):  
Poisson Process ◽  
Arrival Rate ◽  
Loss Probability ◽  
Arrival Process ◽  
Single Server ◽  
Single Server Queue ◽  
Markov Modulated Poisson Process ◽  
Server Queue ◽  
Monotonicity Result ◽  
Markov Modulated

Consider a single-server queue with zero buffer. The arrival process is a three-level Markov modulated Poisson process with an arbitrary transition matrix. The time the system remains at level i (i = 1, 2, 3) is exponentially distributed with rate cα i. The arrival rate at level i is λ i and the service time is exponentially distributed with rate μ i. In this paper we first derive an explicit formula for the loss probability and then prove that it is decreasing in the parameter c. This proves a conjecture of Ross and Rolski's for a single-server queue with zero buffer.

A monotonicity result for a single-server loss system

1995 ◽  
Vol 32 (04) ◽  
pp. 1112-1117
Author(s):  
Xiuli Chao ◽  
Liyi Dai
Keyword(s):  
Markov Process ◽  
Infinitesimal Generator ◽  
Blocking Probability ◽  
Matrix Analysis ◽  
Service Process ◽  
Single Server ◽  
Loss System ◽  
Special Cases ◽  
Monotonicity Result ◽  
Loss Systems

We consider a family of M(t)/M(t)/1/1 loss systems with arrival and service intensities (λt (c), μt (c)) = (λct , μct ), where (λt , μt ) are governed by an irreducible Markov process with infinitesimal generator Q = (qij )m × m such that (λt , μt ) = (λi , μi ) when the Markov process is in state i. Based on matrix analysis we show that the blocking probability is decreasing in c in the interval [0, c ∗], where c ∗ = 1/maxi Σ j ≠i qij /(λi + μi ). Two special cases are studied for which the result can be extended to all c. These results support Ross's conjecture that a more regular arrival (and service) process leads to a smaller blocking probability.

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