Sample path methods in the control of queues

1995 ◽  
Vol 21 (3-4) ◽  
pp. 293-335 ◽  
Author(s):  
Zhen Liu ◽  
Philippe Nain ◽  
Don Towsley
Keyword(s):  
Sample Path ◽  
Control Of Queues

scholarly journals A MARKOV PROCESS OF GENE FREQUENCY CHANGE IN A GEOGRAPHICALLY STRUCTURED POPULATION

Genetics ◽  
1974 ◽  
Vol 76 (2) ◽  
pp. 367-377
Author(s):  
Takeo Maruyama
Keyword(s):  
Genetic Variation ◽  
Markov Process ◽  
Diffusion Process ◽  
Gene Frequency ◽  
Transition Probabilities ◽  
Large Population ◽  
Sample Path ◽  
Time Parameter ◽  
Frequency Change ◽  
Structured Population

ABSTRACT A Markov process (chain) of gene frequency change is derived for a geographically-structured model of a population. The population consists of colonies which are connected by migration. Selection operates in each colony independently. It is shown that there exists a stochastic clock that transforms the originally complicated process of gene frequency change to a random walk which is independent of the geographical structure of the population. The time parameter is a local random time that is dependent on the sample path. In fact, if the alleles are selectively neutral, the time parameter is exactly equal to the sum of the average local genetic variation appearing in the population, and otherwise they are approximately equal. The Kolmogorov forward and backward equations of the process are obtained. As a limit of large population size, a diffusion process is derived. The transition probabilities of the Markov chain and of the diffusion process are obtained explicitly. Certain quantities of biological interest are shown to be independent of the population structure. The quantities are the fixation probability of a mutant, the sum of the average local genetic variation and the variation summed over the generations in which the gene frequency in the whole population assumes a specified value.

scholarly journals Bootstrap joint prediction regions for sequences of missing values in spatio-temporal datasets

2021 ◽  
Author(s):  
Maria Lucia Parrella ◽  
Giuseppina Albano ◽  
Cira Perna ◽  
Michele La Rocca
Keyword(s):  
Missing Data ◽  
Missing Values ◽  
Sample Selection ◽  
Sample Path ◽  
Temporal Relationships ◽  
Empirical Performance ◽  
Spatio Temporal ◽  
Joint Prediction ◽  
Point Forecast ◽  
Prediction Regions

AbstractMissing data reconstruction is a critical step in the analysis and mining of spatio-temporal data. However, few studies comprehensively consider missing data patterns, sample selection and spatio-temporal relationships. To take into account the uncertainty in the point forecast, some prediction intervals may be of interest. In particular, for (possibly long) missing sequences of consecutive time points, joint prediction regions are desirable. In this paper we propose a bootstrap resampling scheme to construct joint prediction regions that approximately contain missing paths of a time components in a spatio-temporal framework, with global probability $$1-\alpha $$ 1 - α . In many applications, considering the coverage of the whole missing sample-path might appear too restrictive. To perceive more informative inference, we also derive smaller joint prediction regions that only contain all elements of missing paths up to a small number k of them with probability $$1-\alpha $$ 1 - α . A simulation experiment is performed to validate the empirical performance of the proposed joint bootstrap prediction and to compare it with some alternative procedures based on a simple nominal coverage correction, loosely inspired by the Bonferroni approach, which are expected to work well standard scenarios.

A Classified Bibliography of Research on Optimal Design and Control of Queues

1977 ◽  
Vol 25 (2) ◽  
pp. 219-232 ◽  
Author(s):  
Thomas B. Crabill ◽  
Donald Gross ◽  
Michael J. Magazine
Keyword(s):  
Optimal Design ◽  
Control Of Queues ◽  
And Control ◽  
Optimal Design And Control

Some analyses on the control of queues using level crossings of regenerative processes

1980 ◽  
Vol 17 (3) ◽  
pp. 814-821 ◽  
Author(s):  
J. G. Shanthikumar
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Queueing Systems ◽  
Density Functions ◽  
Waiting Time Distribution ◽  
Regenerative Processes ◽  
Stieltjes Transform ◽  
Expected Number ◽  
Control Of Queues ◽  
Special Case

Some properties of the number of up- and downcrossings over level u, in a special case of regenerative processes are discussed. Two basic relations between the density functions and the expected number of upcrossings of this process are derived. Using these reults, two examples of controlled M/G/1 queueing systems are solved. Simple relations are derived for the waiting time distribution conditioned on the phase of control encountered by an arriving customer. The Laplace-Stieltjes transform of the distribution function of the waiting time of an arbitrary customer is also derived for each of these two examples.

Simple Bounds and Monotnicity the Call Congestion of Finite Multiserver Delay Systems

1988 ◽  
Vol 2 (1) ◽  
pp. 129-138 ◽  
Author(s):  
Nico M van Dijk ◽  
Pantelis Tsoucas ◽  
Jean Walrand
Keyword(s):  
Optimal Design ◽  
Sample Path ◽  
Upper Bounds ◽  
Monotonicity Property ◽  
Delay Systems ◽  
Asymptotic Result ◽  
Lower And Upper Bounds ◽  
Waiting Room ◽  
Numerical Evidence ◽  
Simple Bounds

Simple and insensitive lower and upper bounds are proposed for the call congestion of M/GI/c/n queues. To prove them we establish the general monotonicity property that increasing the waiting room and/or the number of servers in a /GI/c/n queue increases the throughput. An asymptotic result on the number of busy servers is obtained as a consequence of the bounds. Numerical evidence as well as an application to optimal design illustrates the potential usefulness for engineering purposes. The proof is based on a sample path argument.

Inequalities for the M/G/∞ queue and related shot noise processes

1987 ◽  
Vol 24 (04) ◽  
pp. 978-989 ◽  
Author(s):  
Fred W. Huffer
Keyword(s):  
Poisson Process ◽  
Shot Noise ◽  
Convex Functions ◽  
Sample Path ◽  
Noise Process ◽  
Shot Noise Process

Suppose that pulses arrive according to a Poisson process of rate λ with the duration of each pulse independently chosen from a distribution F having finite mean. Let X(t) be the shot noise process formed by the superposition of these pulses. We consider functionals H(X) of the sample path of X(t). H is said to be L-superadditive if for all functions f and g. For any distribution F for the pulse durations, we define H(F) = EH(X). We prove that if H is L-superadditive and for all convex functions ϕ, then . Various consequences of this result are explored.

Technical Note—Capacitated Serial Inventory Systems: Sample Path and Stability Properties Under Base-Stock Policies

2010 ◽  
Vol 58 (4-part-1) ◽  
pp. 1017-1022 ◽  
Author(s):  
Woonghee Tim Huh ◽  
Ganesh Janakiraman ◽  
Mahesh Nagarajan
Keyword(s):  
Sample Path ◽  
Technical Note ◽  
Inventory Systems ◽  
Base Stock ◽  
Stability Properties ◽  
Base Stock Policies

Sample-path average optimality for Markov control processes

1999 ◽  
Vol 44 (10) ◽  
pp. 1966-1971 ◽  
Author(s):  
J.B. Lasserre
Keyword(s):  
Sample Path ◽  
Control Processes ◽  
Markov Control Processes ◽  
Markov Control

Sample path behaviour of Χ2 surfaces at extrema

1988 ◽  
Vol 20 (4) ◽  
pp. 719-738 ◽  
Author(s):  
Michael Aronowich ◽  
Robert J. Adler
Keyword(s):  
Rough Surfaces ◽  
Sample Path ◽  
Gaussian Field ◽  
Random Surfaces ◽  
Sample Path Properties ◽  
Low Levels ◽  
Path Properties

We study the sample path properties of χ2 random surfaces, in particular in the neighbourhood of their extrema. We show that, as is the case for their Gaussian counterparts, χ2 surfaces at high levels follow the form of certain deterministic paraboloids, but that, unlike their Gaussian counterparts, at low levels their form is much more random. This has a number of interesting implications in the modelling of rough surfaces and the study of the ‘robustness' of Gaussian field models. The general approach of the paper is the study of extrema via the ‘Slepian model process', which, for χ2 fields, is tractable only at asymptotically high or low levels.

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