Optimal bulking threshold of batch service queues

2017 ◽  
Vol 54 (2) ◽  
pp. 409-423 ◽  
Author(s):  
Yun Zeng ◽  
Cathy Honghui Xia
Keyword(s):  
Communication Networks ◽  
Waiting Time ◽  
Renewal Theory ◽  
Simple Algorithm ◽  
Critical Issue ◽  
Batch Service ◽  
Mean Waiting Time ◽  
Batch Service Queues ◽  
Expected Waiting Time ◽  
Necessary And Sufficient

Abstract Batch service has a wide application in manufacturing, communication networks, and cloud computing. In batch service queues with limited resources, one critical issue is to properly schedule the service so as to ensure the quality of service. In this paper we consider an M/G[a,b]/1/N batch service queue with bulking threshold a, max service capacity b, and buffer capacity N, where N can be finite or infinite. Through renewal theory, busy period analysis and decomposition techniques, we demonstrate explicitly how the bulking threshold influences the system performance such as the mean waiting time and time-averaged number of loss customers in batch service queues. We then establish a necessary and sufficient condition on the optimal bulking threshold that minimizes the expected waiting time. Enabled by this condition, we propose a simple algorithm which guarantees to find the optimal threshold in polynomial time. The performance of the algorithm is also demonstrated by numerical examples.

scholarly journals Some reflections on the Renewal-theory paradox in queueing theory

1998 ◽  
Vol 11 (3) ◽  
pp. 355-368 ◽  
Author(s):  
Robert B. Cooper ◽  
Shun-Chen Niu ◽  
Mandyam M. Srinivasan
Keyword(s):  
Waiting Time ◽  
Queueing Theory ◽  
Waiting Times ◽  
Renewal Theory ◽  
Vacation Models ◽  
Polling Models ◽  
Mean Waiting Time ◽  
The Mean ◽  
Expository Paper ◽  
Set Up

The classical renewal-theory (waiting time, or inspection) paradox states that the length of the renewal interval that covers a randomly-selected time epoch tends to be longer than an ordinary renewal interval. This paradox manifests itself in numerous interesting ways in queueing theory, a prime example being the celebrated Pollaczek-Khintchine formula for the mean waiting time in the M/G/1 queue. In this expository paper, we give intuitive arguments that “explain” why the renewal-theory paradox is ubiquitous in queueing theory, and why it sometimes produces anomalous results. In particular, we use these intuitive arguments to explain decomposition in vacation models, and to derive formulas that describe some recently-discovered counterintuitive results for polling models, such as the reduction of waiting times as a consequence of forcing the server to set up even when no work is waiting.

Server unavailability reduces mean waiting time in some batch service queuing systems

1997 ◽  
Vol 24 (6) ◽  
pp. 559-567 ◽  
Author(s):  
H.W. Lee ◽  
D.I. Chung ◽  
S.S. Lee ◽  
K.C. Chae
Keyword(s):  
Waiting Time ◽  
Batch Service ◽  
Queuing Systems ◽  
Mean Waiting Time

scholarly journals Delay Analysis of anM/G/1/KPriority Queueing System with Push-out Scheme

2007 ◽  
Vol 2007 ◽  
pp. 1-12 ◽  
Author(s):  
Yutae Lee ◽  
Bong Dae Choi ◽  
Bara Kim ◽  
Dan Keun Sung
Keyword(s):  
Communication Networks ◽  
Waiting Time ◽  
Queueing System ◽  
Waiting Times ◽  
Loss Probability ◽  
Mean Waiting Time ◽  
The Mean ◽  
Recursive Equations ◽  
Push Out ◽  
Stieltjes Transforms

This paper considers anM/G/1/Kqueueing system with push-out scheme which is one of the loss priority controls at a multiplexer in communication networks. The loss probability for the model with push-out scheme has been analyzed, but the waiting times are not available for the model. Using a set of recursive equations, this paper derives the Laplace-Stieltjes transforms (LSTs) of the waiting time and the push-out time of low-priority messages. These results are then utilized to derive the loss probability of each traffic type and the mean waiting time of high-priority messages. Finally, some numerical examples are provided.

493 Evaluation of Patient Waiting Times for Plain Radiographs Whilst Attending Outpatient Clinics in A Tertiary Orthopaedic Centre

2021 ◽  
Vol 108 (Supplement_2) ◽  
Author(s):  
Z Hayat ◽  
E Kinene ◽  
S Molloy
Keyword(s):  
Waiting Time ◽  
Waiting Times ◽  
Time Frame ◽  
Outpatient Clinics ◽  
Contributing Factors ◽  
Time Data ◽  
Work Related ◽  
Mean Waiting Time ◽  
Appointment Time ◽  
Related Stress

Abstract Introduction Reduction of waiting times is key to delivering high quality, efficient health care. Delays experienced by patients requiring radiographs in orthopaedic outpatient clinics are well recognised. Method To establish current patient and staff satisfaction, questionnaires were circulated over a two-week period. Waiting time data was retrospectively collected including appointment time, arrival time and the time at which radiographs were taken. Results 84% (n = 16) of radiographers believed patients would be dissatisfied. However, of the 296 patients questioned, 56% (n = 165) were satisfied. Most patients (89%) felt the waiting time should be under 30 minutes. Only 36% were seen in this time frame. There was moderate negative correlation (R=-0.5); higher waiting times led to increased dissatisfaction. Mean waiting time was 00:37 and the maximum 02:48. Key contributing factors included volume of patients, staff shortages (73.7%), equipment shortages (57.9%) and incorrectly filled request forms. Eight (42.1%) had felt unwell from work related stress. Conclusions A concerted effort is needed to improve staff and patient opinion. There is scope for change post COVID. Additional training and exploring ways to avoid overburdening the department would benefit. Numerous patients were open to different days or alternative sites. Funding requirements make updating equipment, expanding the department and recruiting more staff challenging.

HOW TO REPORT AND MONITOR THE PERFORMANCE OF WAITING LIST MANAGEMENT

2002 ◽  
Vol 18 (3) ◽  
pp. 611-618
Author(s):  
Markus Torkki ◽  
Miika Linna ◽  
Seppo Seitsalo ◽  
Pekka Paavolainen
Keyword(s):  
Hallux Valgus ◽  
Waiting Time ◽  
Varicose Vein ◽  
Elective Surgery ◽  
Waiting Times ◽  
Waiting List ◽  
Mean Waiting Time ◽  
Number Of Patients ◽  
Potential Problems ◽  
Queue Discipline

Objectives: Potential problems concerning waiting list management are often monitored using mean waiting times based on empirical samples. However, the appropriateness of mean waiting time as an indicator of access can be questioned if a waiting list is not managed well, e.g., if the queue discipline is violated. This study was performed to find out about the queue discipline in waiting lists for elective surgery to reveal potential discrepancies in waiting list management. Methods: There were 1,774 waiting list patients for hallux valgus or varicose vein surgery or sterilization. The waiting time distributions of patients receiving surgery and of patients still waiting for an operation are presented in column charts. The charts are compared with two model charts. One model chart presents a high queue discipline (first in—first out) and another a poor queue discipline (random) queue. Results: There were significant differences in waiting list management across hospitals and patient categories. Examples of a poor queue discipline were found in queues for hallux valgus and varicose vein operations. Conclusions: A routine waiting list reporting should be used to guarantee the quality of waiting list management and to pinpoint potential problems in access. It is important to monitor not only the number of patients in the waiting list but also the queue discipline and the balance between demand and supply of surgical services. The purpose for this type of reporting is to ensure that the priority setting made at health policy level also works in practise.

Estimating waiting and idle times for special queuing situations of tree harvesting machines

1981 ◽  
Vol 11 (1) ◽  
pp. 99-104 ◽  
Author(s):  
C. H. Meng
Keyword(s):  
Waiting Time ◽  
Historical Data ◽  
Idle Time ◽  
Processing Times ◽  
Mean Waiting Time ◽  
Analytical Formulae ◽  
Input Time ◽  
Time Required ◽  
Tree Harvesting ◽  
Normally Distributed

The purpose of this study is to develop analytical formulae for special queuing situations which occur during the operations of the felling and processing devices of a tree harvester, and the pickup and processing devices of a tree processor. Analytical formulae are used to estimate mean waiting time and mean idle time; in case 1 both "input" times and processing times are normally distributed; in case 2 "input" times are normally distributed and processing times are Poisson distributed. "Input" time is a term used for convenience to denote time required to fell a tree by a harvester or time required to pick up a tree by a processor. Methods of choosing distributions for representing "input" times and processing times are provided. In addition, there are two examples, using historical data, which demonstrate the applications of the analytical formulae.

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

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