A diffusion approximation for correlation in queues

1980 ◽  
Vol 17 (04) ◽  
pp. 1033-1047 ◽  
Author(s):  
C. M. Woodside ◽  
B. Pagurek ◽  
G. F. Newell
Keyword(s):  
Waiting Time ◽  
Probability Distributions ◽  
Heavy Traffic ◽  
Waiting Times ◽  
Queueing Systems ◽  
Spectral Density Function ◽  
Percentage Error ◽  
Similar Accuracy ◽  
System Time ◽  
Infinite Sum

A diffusion model is used to find heavy traffic approximate autocorrelation functions for several variables in queueing systems (i.e. for waiting time, system time, number in system and unfinished work). A table is given by which correlations can easily be found for each variable in anyGI/G/1 queue. Further, the infinite sum or integral of the autocorrelations is also found, and the spectral density function. The sum has applications in statistical analysis of queues.Extensive comparisons of approximate and exact correlations and their sums are reported, particularly for waiting times and system times, but also including number in system inM/M/1 queues. In general the correlations have similar accuracy to the probability distributions found by diffusion approximations. The percentage error is less for number in system than for waiting time.

A diffusion approximation for correlation in queues

1980 ◽  
Vol 17 (4) ◽  
pp. 1033-1047 ◽  
Author(s):  
C. M. Woodside ◽  
B. Pagurek ◽  
G. F. Newell
Keyword(s):  
Waiting Time ◽  
Probability Distributions ◽  
Heavy Traffic ◽  
Waiting Times ◽  
Queueing Systems ◽  
Spectral Density Function ◽  
Percentage Error ◽  
Similar Accuracy ◽  
System Time ◽  
Infinite Sum

A diffusion model is used to find heavy traffic approximate autocorrelation functions for several variables in queueing systems (i.e. for waiting time, system time, number in system and unfinished work). A table is given by which correlations can easily be found for each variable in any GI/G/1 queue. Further, the infinite sum or integral of the autocorrelations is also found, and the spectral density function. The sum has applications in statistical analysis of queues.Extensive comparisons of approximate and exact correlations and their sums are reported, particularly for waiting times and system times, but also including number in system in M/M/1 queues. In general the correlations have similar accuracy to the probability distributions found by diffusion approximations. The percentage error is less for number in system than for waiting time.

The virtual waiting time of the GI/G/1 queue in heavy traffic

1971 ◽  
Vol 3 (2) ◽  
pp. 249-268 ◽  
Author(s):  
E. Kyprianou
Keyword(s):  
Markov Chains ◽  
Waiting Time ◽  
Limit Theorems ◽  
Queueing System ◽  
Heavy Traffic ◽  
Waiting Times ◽  
Double Sequence ◽  
Traffic Intensity ◽  
Virtual Waiting Time

Investigations in the theory of heavy traffic were initiated by Kingman ([5], [6] and [7]) in an effort to obtain approximations for stable queues. He considered the Markov chains {Wni} of a sequence {Qi} of stable GI/G/1 queues, where Wni is the waiting time of the nth customer in the ith queueing system, and by making use of Spitzer's identity obtained limit theorems as first n → ∞ and then ρi ↑ 1 as i → ∞. Here &rHi is the traffic intensity of the ith queueing system. After Kingman the theory of heavy traffic was developed by a number of Russians mainly. Prohorov [10] considered the double sequence of waiting times {Wni} and obtained limit theorems in the three cases when n1/2(ρi-1) approaches (i) - ∞, (ii) -δ and (iii) 0 as n → ∞ and i → ∞ simultaneously. The case (i) includes the result of Kingman. Viskov [12] also studied the double sequence {Wni} and obtained limits in the two cases when n1/2(ρi − 1) approaches + δ and + ∞ as n → ∞ and i → ∞ simultaneously.

Some comparability results for waiting times in single- and many-server queues

1984 ◽  
Vol 21 (4) ◽  
pp. 887-900 ◽  
Author(s):  
D. J. Daley ◽  
T. Rolski
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Waiting Times ◽  
Queueing Systems ◽  
Random Variables ◽  
Interarrival Time ◽  
Sufficient Condition ◽  
Traffic Intensity ◽  
Many Server Queues ◽  
Stationary Waiting Time

It is shown that the stationary waiting time random variables W′, W″ of two M/G/l queueing systems for which the corresponding service time random variables satisfy E(S′−x)+ ≦ E(S″−x)+ (all x >0), are stochastically ordered as W′≦dW″. The weaker conclusion, that E(W′−x)+ ≦ E(W″−x)+ (all x > 0), is shown to hold in GI/M/k systems when the interarrival time random variables satisfy E(x−T′)+ ≦ E(x−T″)+ (all x). A sufficient condition for wk≡EW in GI/D/k to be monotonic in k for a sequence of k-server queues with the same relative traffic intensity is given. Evidence indicating or refuting possible strengthenings of some of the results is indicated.

scholarly journals A result in queueing theory

1978 ◽  
Vol 19 (1) ◽  
pp. 125-129
Author(s):  
A. Ghosal
Keyword(s):  
Waiting Time ◽  
Queueing Theory ◽  
Waiting Times ◽  
Queueing Systems ◽  
Random Variable ◽  
Equilibrium Distribution Function ◽  
Single Server ◽  
Queue Discipline ◽  
The Difference ◽  
Practical Implications

In a single-server queueing system, subject to the queue discipline ‘First come first served’, the equilibrium distribution function of the waiting time of a server depends on the distribution of the random variable (u) which is the difference between the service time and the inter-arrival time. If in two queueing systems u's are equivalent in distribution, the waiting times are also equivalent in distribution (known result). It has been shown in this note that equivalence in waiting time distributions does not necessarily imply equivalence in distributions of u's. The proof is heuristic. This result has useful practical implications.

The virtual waiting time of the GI/G/1 queue in heavy traffic

1971 ◽  
Vol 3 (02) ◽  
pp. 249-268 ◽  
Author(s):  
E. Kyprianou
Keyword(s):  
Markov Chains ◽  
Waiting Time ◽  
Limit Theorems ◽  
Queueing System ◽  
Heavy Traffic ◽  
Waiting Times ◽  
Double Sequence ◽  
Traffic Intensity ◽  
Virtual Waiting Time

Investigations in the theory of heavy traffic were initiated by Kingman ([5], [6] and [7]) in an effort to obtain approximations for stable queues. He considered the Markov chains {W n i } of a sequence {Q i } of stable GI/G/1 queues, where W n i is the waiting time of the nth customer in the ith queueing system, and by making use of Spitzer's identity obtained limit theorems as first n → ∞ and then ρ i ↑ 1 as i → ∞. Here &rH i is the traffic intensity of the ith queueing system. After Kingman the theory of heavy traffic was developed by a number of Russians mainly. Prohorov [10] considered the double sequence of waiting times {W n i } and obtained limit theorems in the three cases when n 1/2(ρ i -1) approaches (i) - ∞, (ii) -δ and (iii) 0 as n → ∞ and i → ∞ simultaneously. The case (i) includes the result of Kingman. Viskov [12] also studied the double sequence {W n i } and obtained limits in the two cases when n 1/2(ρ i − 1) approaches + δ and + ∞ as n → ∞ and i → ∞ simultaneously.

Some comparability results for waiting times in single- and many-server queues

1984 ◽  
Vol 21 (04) ◽  
pp. 887-900 ◽  
Author(s):  
D. J. Daley ◽  
T. Rolski
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Waiting Times ◽  
Queueing Systems ◽  
Random Variables ◽  
Interarrival Time ◽  
Sufficient Condition ◽  
Traffic Intensity ◽  
Many Server Queues ◽  
Stationary Waiting Time

It is shown that the stationary waiting time random variables W′, W″ of two M/G/l queueing systems for which the corresponding service time random variables satisfy E(S ′−x)+ ≦ E(S ″−x)+ (all x >0), are stochastically ordered as W ′≦d W ″. The weaker conclusion, that E(W ′−x)+ ≦ E(W ″−x)+ (all x > 0), is shown to hold in GI/M/k systems when the interarrival time random variables satisfy E(x−T ′)+ ≦ E(x−T ″)+ (all x). A sufficient condition for wk ≡EW in GI/D/k to be monotonic in k for a sequence of k-server queues with the same relative traffic intensity is given. Evidence indicating or refuting possible strengthenings of some of the results is indicated.

scholarly journals Interhospital referral of colorectal cancer patients: a Dutch population-based study

2021 ◽  
Author(s):  
A. K. Warps ◽  
◽  
M. P. M. de Neree tot Babberich ◽  
E. Dekker ◽  
M. W. J. M. Wouters ◽  
...  
Keyword(s):  
Colorectal Cancer ◽  
Cancer Patients ◽  
Waiting Time ◽  
Secondary Care ◽  
Advanced Disease ◽  
Waiting Times ◽  
Tertiary Care ◽  
Disease Stage ◽  
Colorectal Cancer Patients ◽  
Tertiary Care Hospitals

Abstract Purpose Interhospital referral is a consequence of centralization of complex oncological care but might negatively impact waiting time, a quality indicator in the Netherlands. This study aims to evaluate characteristics and waiting times of patients with primary colorectal cancer who are referred between hospitals. Methods Data were extracted from the Dutch ColoRectal Audit (2015-2019). Waiting time between first tumor-positive biopsy until first treatment was compared between subgroups stratified for referral status, disease stage, and type of hospital. Results In total, 46,561 patients were included. Patients treated for colon or rectal cancer in secondary care hospitals were referred in 12.2% and 14.7%, respectively. In tertiary care hospitals, corresponding referral rates were 43.8% and 66.4%. Referred patients in tertiary care hospitals were younger, but had a more advanced disease stage, and underwent more often multivisceral resection and simultaneous metastasectomy than non-referred patients in secondary care hospitals (p<0.001). Referred patients were more often treated within national quality standards for waiting time compared to non-referred patients (p<0.001). For referred patients, longer waiting times prior to MDT were observed compared to non-referred patients within each hospital type, although most time was spent post-MDT. Conclusion A large proportion of colorectal cancer patients that are treated in tertiary care hospitals are referred from another hospital but mostly treated within standards for waiting time. These patients are younger but often have a more advanced disease. This suggests that these patients are willing to travel more but also reflects successful centralization of complex oncological patients in the Netherlands.

scholarly journals E-Triage Systems for COVID-19 Outbreak: Review and Recommendations

Sensors ◽  
2021 ◽  
Vol 21 (8) ◽  
pp. 2845
Author(s):  
Fahd Alhaidari ◽  
Abdullah Almuhaideb ◽  
Shikah Alsunaidi ◽  
Nehad Ibrahim ◽  
Nida Aslam ◽  
...  
Keyword(s):  
Population Growth ◽  
Disease Severity ◽  
Waiting Time ◽  
Transmission Rate ◽  
Waiting Times ◽  
Triage System ◽  
Disease Symptoms ◽  
Comprehensive Review ◽  
Severity Levels ◽  
Growth And Aging

With population growth and aging, the emergence of new diseases and immunodeficiency, the demand for emergency departments (EDs) increases, making overcrowding in these departments a global problem. Due to the disease severity and transmission rate of COVID-19, it is necessary to provide an accurate and automated triage system to classify and isolate the suspected cases. Different triage methods for COVID-19 patients have been proposed as disease symptoms vary by country. Still, several problems with triage systems remain unresolved, most notably overcrowding in EDs, lengthy waiting times and difficulty adjusting static triage systems when the nature and symptoms of a disease changes. In this paper, we conduct a comprehensive review of general ED triage systems as well as COVID-19 triage systems. We identified important parameters that we recommend considering when designing an e-Triage (electronic triage) system for EDs, namely waiting time, simplicity, reliability, validity, scalability, and adaptability. Moreover, the study proposes a scoring-based e-Triage system for COVID-19 along with several recommended solutions to enhance the overall outcome of e-Triage systems during the outbreak. The recommended solutions aim to reduce overcrowding and overheads in EDs by remotely assessing patients’ conditions and identifying their severity levels.

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