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 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

Queuing models for wireless mesh networks

2013 ◽  
Vol 18 (4) ◽  
pp. 21-31
Author(s):  
Sławomir Hanczewski ◽  
Maciej Sobieraj ◽  
Michał Dominik Stasiak ◽  
Joanna Weissenberg
Keyword(s):  
Wireless Mesh Networks ◽  
Waiting Time ◽  
Queue Length ◽  
Mesh Networks ◽  
Mesh Network ◽  
Queueing Models ◽  
Average Waiting Time ◽  
Multiservice Networks ◽  
Queuing Models ◽  
Wireless Mesh

Abstract In this paper we discuss a proposition of various applications of new queueing models that have been developed within the CARMNET project in nodes of the mesh network. These models allow characteristics of systems that service multi-rate traffic to be determined, e.g., the average queue length or the average waiting time for calls of a given class. The proposed models can be used to design, analyse and optimize multiservice networks

Some general results for many server queues

1973 ◽  
Vol 5 (01) ◽  
pp. 153-169 ◽  
Author(s):  
J. H. A. De Smit
Keyword(s):  
Integral Equations ◽  
Waiting Time ◽  
Queue Length ◽  
Joint Distribution ◽  
Waiting Times ◽  
Virtual Waiting Time ◽  
Server Queue ◽  
Many Server Queues ◽  
The Many ◽  
Busy Cycle

Pollaczek's theory for the many server queue is generalized and extended. Pollaczek (1961) found the distribution of the actual waiting times in the model G/G/s as a solution of a set of integral equations. We give a somewhat more general set of integral equations from which the joint distribution of the actual waiting time and some other random variables may be found. With this joint distribution we can obtain distributions of a number of characteristic quantities, such as the virtual waiting time, the queue length, the number of busy servers, the busy period and the busy cycle. For a wide class of many server queues the formal expressions may lead to explicit results.

scholarly journals Decoupled evolution of soft and hard substrate communities during the Cambrian Explosion and Great Ordovician Biodiversification Event

2016 ◽  
Vol 113 (25) ◽  
pp. 6945-6948 ◽  
Author(s):  
Luis A. Buatois ◽  
Maria G. Mángano ◽  
Ricardo A. Olea ◽  
Mark A. Wilson
Keyword(s):  
Late Ordovician ◽  
Hard Substrate ◽  
Cambrian Explosion ◽  
Early Cambrian ◽  
Continuous Increase ◽  
Late Cambrian ◽  
Unconsolidated Sediment ◽  
Underlying Causes ◽  
Hard Substrates ◽  
Shed Light

Contrasts between the Cambrian Explosion (CE) and the Great Ordovician Biodiversification Event (GOBE) have long been recognized. Whereas the vast majority of body plans were established as a result of the CE, taxonomic increases during the GOBE were manifested at lower taxonomic levels. Assessing changes of ichnodiversity and ichnodisparity as a result of these two evolutionary events may shed light on the dynamics of both radiations. The early Cambrian (series 1 and 2) displayed a dramatic increase in ichnodiversity and ichnodisparity in softground communities. In contrast to this evolutionary explosion in bioturbation structures, only a few Cambrian bioerosion structures are known. After the middle to late Cambrian diversity plateau, ichnodiversity in softground communities shows a continuous increase during the Ordovician in both shallow- and deep-marine environments. This Ordovician increase in bioturbation diversity was not paralleled by an equally significant increase in ichnodisparity as it was during the CE. However, hard substrate communities were significantly different during the GOBE, with an increase in ichnodiversity and ichnodisparity. Innovations in macrobioerosion clearly lagged behind animal–substrate interactions in unconsolidated sediment. The underlying causes of this evolutionary decoupling are unclear but may have involved three interrelated factors: (i) a Middle to Late Ordovician increase in available hard substrates for bioerosion, (ii) increased predation, and (iii) higher energetic requirements for bioerosion compared with bioturbation.

Estimating Rates and Probabilities of Origination and Extinction Using Taxonomic Occurrence Data: Capture-Mark-Recapture (CMR) Approaches

2010 ◽  
Vol 16 ◽  
pp. 81-94 ◽  
Author(s):  
Lee Hsiang Liow ◽  
James D. Nichols
Keyword(s):  
Simultaneous Estimation ◽  
Mark Recapture ◽  
Sampling Process ◽  
Occurrence Data ◽  
Geographical Regions ◽  
Underlying Causes ◽  
Inherent Problem ◽  
Sampling Probability ◽  
Shed Light ◽  
Replicate Sampling

We rely on observations of occurrences of fossils to infer the rates and timings of origination and extinction of taxa. These estimates can then be used to shed light on questions such as whether extinction and origination rates have been higher or lower at different times in earth history or in different geographical regions, etc. and to investigate the possible underlying causes of varying rates. An inherent problem in inference using occurrence data is one of incompleteness of sampling. Even if a taxon is present at a given time and place, we are guaranteed to detect or sample it less than 100% of the time we search in a random outcrop or sediment sample that should contain it, either because it was not preserved, it was preserved but then eroded, or because we simply did not find it. Capture-mark-recapture (CMR) methods rely on replicate sampling to allow for the simultaneous estimation of sampling probability and the parameters of interest (e.g. extinction, origination, occupancy, diversity). Here, we introduce the philosophy of CMR approaches especially as applicable to paleontological data and questions. The use of CMR is in its infancy in paleobiological applications, but the handful of studies that have used it demonstrate its utility and generality. We discuss why the use of CMR has not matched its development in other fields, such as in population ecology, as well as the importance of modelling the sampling process and estimating sampling probabilities. In addition, we suggest some potential avenues for the development of CMR applications in paleobiology.

scholarly journals Development of a Priority based System for Emergency Vehicles to Reduce Accidents in VANETs

2020 ◽  
Vol 9 (2) ◽  
pp. 483-486
Keyword(s):  
Waiting Time ◽  
Vehicular Ad Hoc Networks ◽  
Ad Hoc ◽  
Human Life ◽  
Traffic Signals ◽  
Emergency Vehicles ◽  
Movement System ◽  
Hoc Networks ◽  
The Cost ◽  
Vehicle Movement

Due to tremendous increase of vehicles in number leads to excessive congestion of vehicles at intersection of roads. It causing inconvenience to emergency vehicles like Ambulance and Fire brigade etc, ultimately which is the cost of human life To avoid this, Emergency Vehicles will have to give high priority to overcome from the congestion. Vehicular Ad-Hoc Networks (VANETs) is a network which is used to create a temporary communication among the vehicles. In this paper, priority based vehicle movement system is proposed to give high priority to emergency vehicles and establishing communication among the vehicles through VANET. Due to this high priority, there is no necessity to wait for the emergency vehicles at the traffic signals to get the green signal while communicating with traffic controller. In this paper, SUMO simulator is used for experimental analysis. The result indicates that the proposed methodology reduces the waiting time when compared to the existing system.

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 Decomposition of M/M/1 With Unreliable Service and a Working Vacation

2020 ◽  
Vol 9 (1) ◽  
pp. 63
Author(s):  
Joshua Patterson ◽  
Andrzej Korzeniowski
Keyword(s):  
Closed Form ◽  
Failure Rate ◽  
Waiting Time ◽  
Queue Length ◽  
Service Failure ◽  
Working Vacation ◽  
Stationary Queue Length ◽  
Stationary Waiting Time ◽  
Relationship Of ◽  
The Relationship

We use the stationary distribution for the M/M/1 with Unreliable Service and aWorking Vacation (M/M/1/US/WV) given explicitly in (Patterson & Korzeniowski, 2019) to find a decomposition of the stationary queue length N. By applying the distributional form of Little's Law the Laplace-tieltjes Transform of the stationary customer waiting time W is derived. The closed form of the expected value and variance for both N and W is found and the relationship of the expected stationary waiting time as a function of the service failure rate is determined.

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