Dynamized routing policies for minimizing expected waiting time in a multi-class multi-server system

Queuing Theory provides the system of applications in many sectors in life cycle. Queuing Structure and basic components determination is computed in queuing model simulation process. Distributions in Queuing Model can be extracted in quantitative analysis approach. Differences in Queuing Model Queue discipline, Single and Multiple service station with finite and infinite population is described in Quantitative analysis process. Basic expansions of probability density function, Expected waiting time in queue, Expected length of Queue, Expected size of system, probability of server being busy, and probability of system being empty conditions can be evaluated in this quantitative analysis approach. Probability of waiting ‘t’ minutes or more in queue and Expected number of customer served per busy period, Expected waiting time in System are also computed during the Analysis method. Single channel model with infinite population is used as most common case of queuing problems which involves the single channel or single server waiting line. Single Server model with finite population in test statistics provides the Relationships used in various applications like Expected time a customer spends in the system, Expected waiting time of a customer in the queue, Probability that there are n customers in the system objective case, Expected number of customers in the system

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Recovery from congestion in a large multi-server system

Teletraffic Science and Engineering - Teletraffic Contributions for the Information Age, Proceedings of the 15th International Teletraffic Congress - ITC 15 ◽

10.1016/s1388-3437(97)80041-8 ◽

1997 ◽

pp. 371-380 ◽

Cited By ~ 2

Author(s):

N.G. Duffield ◽

Ward Whitt

Keyword(s):

Multi Server ◽

Server System

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The Speed of Innovation Diffusion in Social Networks

Econometrica ◽

10.3982/ecta17007 ◽

2020 ◽

Vol 88 (2) ◽

pp. 569-594

Author(s):

Itai Arieli ◽

Yakov Babichenko ◽

Ron Peretz ◽

H. Peyton Young

Keyword(s):

Social Networks ◽

Social Network ◽

Waiting Time ◽

Network Topology ◽

Upper Bound ◽

Status Quo ◽

Arbitrary Size ◽

The Status ◽

Expected Waiting Time ◽

Regular Networks

New ways of doing things often get started through the actions of a few innovators, then diffuse rapidly as more and more people come into contact with prior adopters in their social network. Much of the literature focuses on the speed of diffusion as a function of the network topology. In practice, the topology may not be known with any precision, and it is constantly in flux as links are formed and severed. Here, we establish an upper bound on the expected waiting time until a given proportion of the population has adopted that holds independently of the network structure. Kreindler and Young (2014) demonstrated such a bound for regular networks when agents choose between two options: the innovation and the status quo. Our bound holds for directed and undirected networks of arbitrary size and degree distribution, and for multiple competing innovations with different payoffs.

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Modeling of public transport waiting time indicator for the transport network of a large city

MATEC Web of Conferences ◽

10.1051/matecconf/201822404018 ◽

2018 ◽

Vol 224 ◽

pp. 04018 ◽

Cited By ~ 1

Author(s):

Olga Lebedeva ◽

Marina Kripak

Keyword(s):

Waiting Time ◽

Large City ◽

Distribution Functions ◽

Weibull Function ◽

Explanatory Variables ◽

Transport Services ◽

Time Period ◽

Bus Stops ◽

The Difference ◽

Expected Waiting Time

The need to develop and improve public passenger transport in major cities was noted. It was reflected that waiting time at bus stops is one of the factors that have a big impact on the passenger quality assessment of transport services. The results of an empirical study of the actual and anticipated waiting time at bus stops were given. It was noted that the reliability functions were used in the field of ride duration modeling, traffic restoration time after an accident, and length of making the decision to travel. The waiting time distribution functions using the lognormal function and the Weibull function were chosen. The results of modeling were objective, the dependent variables in it were the expected waiting time of passengers and the difference between the anticipated and the actual waiting time. The explanatory variables were sex, age, time period, purpose of the trip and the actual waiting time. The results of the research showed that the age, purpose of the trip and the time period influence the waiting time perception, prolong it and lead to its reassessment.

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Note: The Value and Cost of the Customer’s Waiting Time

Manufacturing & Service Operations Management ◽

10.1287/msom.2020.0914 ◽

2020 ◽

Author(s):

Rachel R. Chen ◽

Subodha Kumar ◽

Jaya Singhal ◽

Kalyan Singhal

Keyword(s):

Waiting Time ◽

Queue Length ◽

Relative Cost ◽

Queuing Models ◽

Underlying Causes ◽

Two Measures ◽

Expected Waiting Time ◽

The Cost ◽

Shed Light ◽

Key Parameter

The (relative) cost of the customer’s waiting time has long been used as a key parameter in queuing models, but it can be difficult to estimate. A recent study introduced a new queue characteristic, the value of the customer’s waiting time, which measures how an increase in the total customer waiting time reduces the servers’ idle time. This paper connects and contrasts these two fundamental concepts in the queuing literature. In particular, we show that the value can be equal to the cost of waiting when the queue is operated at optimal. In this case, we can use the observed queue length to compute the value of waiting, which helps infer the cost of waiting. Nevertheless, these two measures have very different economic interpretations, and in general, they are not equal. For nonoptimal queues, comparing the value with the cost helps shed light on the underlying causes of the customer’s waiting. Although it is tempting to conclude that customers in a queue with a lower value of waiting expect to wait longer, we find that the value of waiting in general does not have a monotonic relationship with the expected waiting time, nor with the expected queue length.

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Concurrent sequences of Bernoulli trials

The Mathematical Gazette ◽

10.1017/mag.2020.98 ◽

2020 ◽

Vol 104 (561) ◽

pp. 435-448

Author(s):

Stephen Kaczkowski

Keyword(s):

Waiting Time ◽

Waiting Times ◽

Lottery Ticket ◽

Bernoulli Trials ◽

Expectation Values ◽

Theoretical Probability ◽

Expected Waiting Time

Probability and expectation are two distinct measures, both of which can be used to indicate the likelihood of certain events. However, expectation values, which are often associated with waiting times for success, may, at times, speak more clearly and poignantly about the uncertainty of an event than a theoretical probability. To illustrate the point, suppose the probability of choosing a winning lottery ticket is 2.5 × 10−8. This information may not communicate the unlikely odds of winning as clearly as a statement like, “If five lottery tickets are purchased per day, the expected waiting time for a first win is about 22000 years.”

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Simple approximations to the expected waiting time for a cluster of any given size, for point processes

Advances in Applied Probability ◽

10.1017/s0001867800020978 ◽

1983 ◽

Vol 15 (01) ◽

pp. 21-38 ◽

Cited By ~ 2

Author(s):

Ester Samuel-Cahn

Keyword(s):

Waiting Time ◽

Point Processes ◽

Upper Bounds ◽

Poisson Processes ◽

Lower And Upper Bounds ◽

Compound Poisson ◽

Compound Poisson Processes ◽

Interarrival Times ◽

Expected Waiting Time ◽

Simple Points

For point processes, such that the interarrival times of points are independently and identically distributed, let T(L, m) denote the time until at least points cluster within an interval of length at most L. Let τ (L, m) + 1 be the total number of points observed until the above happens. Simple approximations of Eτ (L, m) and ET(L, m) are derived, as well as lower and upper bounds for their value. Approximations to the variances are also given. In particular the Poisson, Bernoulli and compound Poisson processes are discussed in detail. Some numerical tables are included.

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