scholarly journals Confidence limits for expected waiting time of two queuing models

ORiON ◽  
2004 ◽  
Vol 20 (1) ◽  
Author(s):  
VSS Yadavalli ◽  
K Adendorff ◽  
G Erasmus ◽  
P Chandrasekhar ◽  
SP Deepa
Keyword(s):  
Waiting Time ◽  
Confidence Limits ◽  
Queuing Models ◽  
Expected Waiting Time

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

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.

scholarly journals Minimal cost service rate in priority queuing models for emergency cases in hospitals

2018 ◽  
Vol 6 (2) ◽  
pp. 50
Author(s):  
Nse S. Udoh ◽  
Idorenyin A. Etukudo
Keyword(s):  
Waiting Time ◽  
Service Rate ◽  
Time Cost ◽  
Service Cost ◽  
Queuing Model ◽  
Total Cost ◽  
Lower Priority ◽  
Queuing Models ◽  
Optimum Cost ◽  
Expected Waiting Time

Performance measures and waiting time cost for higher priority patients with severe cases over lower priority patients with stable cases using preemptive priority queuing model were obtained. Also, a total expected waiting time cost per unit time for service and the expected service cost per unit time for priority queuing models: M/M/2: ∞/NPP and M/M/2: ∞/PP were respectively formulated and optimized to obtain optimum cost service rate that minimizes the total cost. The results were applied to obtain optimum service rate that minimizes the total cost of providing and waiting for service at the emergency consulting unit of hospital.    

scholarly journals Applications of Queuing Theory in Quantitative Business Analysis

2020 ◽  
pp. 253-257
Keyword(s):  
Quantitative Analysis ◽  
Waiting Time ◽  
Queuing Theory ◽  
Single Channel ◽  
Analysis Approach ◽  
Single Server ◽  
Expected Number ◽  
Queuing Model ◽  
Infinite Population ◽  
Expected Waiting Time

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

scholarly journals The Speed of Innovation Diffusion in Social Networks

Econometrica ◽  
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.

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

2018 ◽  
Vol 224 ◽  
pp. 04018 ◽  
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.

Concurrent sequences of Bernoulli trials

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.”

Measuring the variance of customer waiting time in service operations

2014 ◽  
Vol 52 (2) ◽  
pp. 296-312 ◽  
Author(s):  
Xiaofeng Zhao ◽  
Jianrong Hou ◽  
Kenneth Gilbert
Keyword(s):  
Standard Deviation ◽  
Waiting Time ◽  
Coefficient Of Variation ◽  
Service Operations ◽  
Exact Expression ◽  
Service Industries ◽  
Significant Feature ◽  
Content Type ◽  
Queuing Models ◽  
Spreadsheet Model

Purpose – Waiting lines and delays have become commonplace in service operations. As a result, customer waiting time guarantee is a widely used competition strategy in service industries. To implement waiting time guarantee strategy, managers need to not only know the average of waiting time, but also the variance around average waiting time. This paper aims to discuss these issues. Design/methodology/approach – This research provides a mathematically exact expression for the coefficient of variation of waiting time for Markov queues. It then applies the concept of isomorphism to approximate the variance of customer waiting time in a general queue. Simulation experiments are conducted to verify the accurate approximations. Findings – A significant feature of the approximation method is that it is mathematically tractable and can be implemented in a spreadsheet format. It provides a practical way to estimate the variance of customer waiting time in practice. The results demonstrate the usefulness of the queuing models in providing guidance on implementing appointment scheduling and waiting time guarantee strategy. Also, the spreadsheet can be used to conduct what-if analysis by inputting different parameters. Originality/value – This paper develops a simple, easy-to-use spreadsheet model to estimate the standard deviation of waiting time. The approximation requires only the mean and standard deviation or the coefficient of variation of the inter-arrival and service time distributions, and the number of servers. A spreadsheet model is specifically designed to analyze the variance of waiting time.

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

1983 ◽  
Vol 15 (01) ◽  
pp. 21-38 ◽  
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.

Development of a Heuristics Model for Simplifying a Multi-Channel Queuing System

2011 ◽  
Vol 367 ◽  
pp. 647-652
Author(s):  
B. Kareem ◽  
A. A. Aderoba
Keyword(s):  
Waiting Time ◽  
Channel Model ◽  
Single Channel ◽  
Queuing System ◽  
Queuing Model ◽  
Average Waiting Time ◽  
Queuing Models ◽  
Significant Difference ◽  
Number Of Customers ◽  
Proportionality Principle

Queuing model has been discussed widely in literature. The structures of queuing systems are broadly divided into three namely; single, multi-channel, and mixed. Equations for solving these queuing problems vary in complexity. The most complex of them is the multi-channel queuing problem. A heuristically simplified equation based on relative comparison, using proportionality principle, of the measured effectiveness from the single and multi-channel models seems promising in solving this complex problem. In this study, six different queuing models were used from which five of them are single-channel systems while the balance is multi-channel. Equations for solving these models were identified based on their properties. Queuing models’ performance parameters were measured using relative proportionality principle from which complexity of multi-channel system was transformed to a simple linear relation of the form = . This showed that the performance obtained from single channel model has a linear relationship with corresponding to multi-channel, and is a factor which varies with the structure of queuing system. The model was tested with practical data collected on the arrival and departure of customers from a cocoa processing factory. The performances obtained based on average number of customers on line , average number of customers in the system , average waiting time in line and average waiting time in the system, under certain conditions showed no significant difference between using heuristics and analytical models.

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