On the optimality of LEPT and μc rules for parallel processors and dependent arrival processes

1993 ◽  
Vol 25 (4) ◽  
pp. 979-996 ◽  
Author(s):  
Arie Hordijk ◽  
Ger Koole
Keyword(s):  
Dynamic Programming ◽  
Parallel Processors ◽  
Arrival Process ◽  
Scheduling Problems ◽  
Cost Structures ◽  
Markov Decision ◽  
New Type ◽  
Arrival Processes ◽  
Special Case

In this paper we study scheduling problems of multiclass customers on identical parallel processors. A new type of arrival process, called a Markov decision arrival process, is introduced. This arrival process can be controlled and allows for an indirect dependence on the numbers of customers in the queues. As a special case we show the optimality of LEPT and the µc-rule in the last node of a controlled tandem network for various cost structures. A unifying proof using dynamic programming is given.

On the optimality of LEPT and μc rules for parallel processors and dependent arrival processes

1993 ◽  
Vol 25 (04) ◽  
pp. 979-996
Author(s):  
Arie Hordijk ◽  
Ger Koole
Keyword(s):  
Dynamic Programming ◽  
Parallel Processors ◽  
Arrival Process ◽  
Scheduling Problems ◽  
Cost Structures ◽  
Markov Decision ◽  
New Type ◽  
Arrival Processes ◽  
Special Case

In this paper we study scheduling problems of multiclass customers on identical parallel processors. A new type of arrival process, called a Markov decision arrival process, is introduced. This arrival process can be controlled and allows for an indirect dependence on the numbers of customers in the queues. As a special case we show the optimality of LEPT and the µc-rule in the last node of a controlled tandem network for various cost structures. A unifying proof using dynamic programming is given.

scholarly journals Plurigraph Coloring and Scheduling Problems

10.37236/6818 ◽  
2017 ◽  
Vol 24 (2) ◽  
Author(s):  
John Machacek
Keyword(s):  
Symmetric Function ◽  
Degree Sequence ◽  
Simplicial Complexes ◽  
Vertex Coloring ◽  
Scheduling Problems ◽  
Acyclic Coloring ◽  
New Type ◽  
Star Coloring ◽  
Chromatic Symmetric Function ◽  
Special Case

We define a new type of vertex coloring which generalizes vertex coloring in graphs, hypergraphs, and simplicial complexes. This coloring also generalizes oriented coloring, acyclic coloring, and star coloring. There is an associated symmetric function in noncommuting variables for which we give a deletion-contraction formula. In the case of graphs this symmetric function in noncommuting variables agrees with the chromatic symmetric function in noncommuting variables of Gebhard and Sagan. Our vertex coloring is a special case of the scheduling problems defined by Breuer and Klivans. We show how the deletion-contraction law can be applied to scheduling problems. Also, we show that the chromatic symmetric function determines the degree sequence of uniform hypertrees, but there exists pairs of 3-uniform hypertrees which are not isomorphic yet have the same chromatic symmetric function.

COMPARISON OF QUEUES WITH DIFFERENT DISCRETE-TIME ARRIVAL PROCESSES

2001 ◽  
Vol 15 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Arie Hordijk
Keyword(s):  
Lower Bound ◽  
Discrete Time ◽  
Sojourn Time ◽  
Arrival Process ◽  
Convex Ordering ◽  
Arrival Processes ◽  
Markov Arrival ◽  
Markov Arrival Process ◽  
Special Case ◽  
Stochastic Event

Traveling times in a FIFO-stochastic event graph are compared in increasing convex ordering for different arrival processes. As a special case, a stochastic lower bound is obtained for the sojourn time in a tandem network of FIFO queues with a Markov arrival process. A counterexample shows that the extended Ross conjecture is not true for discrete-time arrival processes.

scholarly journals Scheduling Problems and Generalized Graph Coloring

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
John Machacek
Keyword(s):  
Graph Coloring ◽  
Symmetric Function ◽  
Vertex Coloring ◽  
Scheduling Problems ◽  
International Audience ◽  
New Type ◽  
Chromatic Symmetric Function ◽  
Special Case

International audience We define a new type of vertex coloring which generalizes vertex coloring in graphs, hypergraphs, andsimplicial complexes. To this coloring there is an associated symmetric function in noncommuting variables for whichwe give a deletion-contraction formula. In the case of graphs our symmetric function in noncommuting variablesagrees with the chromatic symmetric function in noncommuting variables of Gebhard and Sagan. Our vertex coloringis a special case of the scheduling problems defined by Breuer and Klivans. We show how the deletion-contractionlaw can be applied to scheduling problems.

Studying Infection Worries by Ecological Momentary Assessment: Development and Causal Factors in Sweden during the Early Phase of the Covid-19 Pandemic (Preprint)

2020 ◽  
Author(s):  
Peter Schulz ◽  
Elin Andersson ◽  
Nicole Bizzotto ◽  
Margareta Norberg
Keyword(s):  
Study Design ◽  
Preventive Action ◽  
Causal Factors ◽  
Perceived Severity ◽  
Assessment Development ◽  
Infection Susceptibility ◽  
The Face ◽  
New Type ◽  
Ecological Momentary ◽  
Special Case

BACKGROUND The foray of Covid-19 around the globe is sure to have instigated worries in many humans, and lockdown measures may well have created their own worries. Sweden, in contrast to most other countries, had first relied on voluntary measures, but had to change its policy in the face of an increasing number of infections. OBJECTIVE The aim was to better understand the worried reactions to the virus and the lockdown measures. To grasp the reactions, their development over time was studied. METHODS Results were based on an unbalanced panel sample of 261 Swedish participants filling in 3218 interview questionnaires by smartphone in a 7-week period in 2020. Causal factors considered in this study include the perceived severity of an infection, the susceptibility of a person to the threat posed by the virus, the perceived efficacy of safeguarding measures and the assessment of government action against the spread of Covid-19. The effect of these factors on worries was traced in two analytical steps: the effects at the beginning of the study, and the effect on the trend during the study. RESULTS Findings confirmed that the hypothesized causal factors (severity of infection, susceptibility to the threat of the virus, efficacy of safeguarding and the assessment of government preventive action did indeed affect worries. CONCLUSIONS The results confirmed earlier research in a very special case and demonstrated the usefulness of a different study design, which takes a longitudinal perspective, and a new type of data analysis borrowed from multi-level study design.

scholarly journals Multi-objective dynamic programming with limited precision

2021 ◽  
Author(s):  
L. Mandow ◽  
J. L. Perez-de-la-Cruz ◽  
N. Pozas
Keyword(s):  
Dynamic Programming ◽  
Pareto Front ◽  
Dynamic Programming Algorithm ◽  
Programming Algorithm ◽  
Value Iteration ◽  
Multi Objective ◽  
All Solutions ◽  
Markov Decision ◽  
Objective Value ◽  
Limited Precision

AbstractThis paper addresses the problem of approximating the set of all solutions for Multi-objective Markov Decision Processes. We show that in the vast majority of interesting cases, the number of solutions is exponential or even infinite. In order to overcome this difficulty we propose to approximate the set of all solutions by means of a limited precision approach based on White’s multi-objective value-iteration dynamic programming algorithm. We prove that the number of calculated solutions is tractable and show experimentally that the solutions obtained are a good approximation of the true Pareto front.

Optimality conditions for a Markov decision chain with unbounded costs

1980 ◽  
Vol 17 (04) ◽  
pp. 996-1003
Author(s):  
D. R. Robinson
Keyword(s):  
Dynamic Programming ◽  
Optimality Conditions ◽  
Average Cost ◽  
Optimality Equation ◽  
Dynamic Programming Equation ◽  
Potential Condition ◽  
Markov Decision ◽  
General Conditions

It is known that when costs are unbounded satisfaction of the appropriate dynamic programming ‘optimality' equation by a policy is not sufficient to guarantee its average optimality. A ‘lowest-order potential' condition is introduced which, along with the dynamic programming equation, is sufficient to establish the optimality of the policy. Also, it is shown that under fairly general conditions, if the lowest-order potential condition is not satisfied there exists a non-memoryless policy with smaller average cost than the policy satisfying the dynamic programming equation.

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