scholarly journals On a Unifying Theory on Polling Models in Heavy Traffic

2007 ◽  
pp. 556-567 ◽  
Author(s):  
R. D. van der Mei
Keyword(s):  
Heavy Traffic ◽  
Polling Models

scholarly journals Heavy-traffic limits for polling models with exhaustive service and non-FCFS service order policies

2015 ◽  
Vol 47 (04) ◽  
pp. 989-1014 ◽  
Author(s):  
P. Vis ◽  
R. Bekker ◽  
R. D. van der Mei
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Heavy Traffic ◽  
Processor Sharing ◽  
Waiting Time Distribution ◽  
Asymptotic Results ◽  
Local Service ◽  
Waiting Time Distributions ◽  
Polling Models ◽  
The Impact

We study cyclic polling models with exhaustive service at each queue under a variety of non-FCFS (first-come-first-served) local service orders, namely last-come-first-served with and without preemption, random-order-of-service, processor sharing, the multi-class priority scheduling with and without preemption, shortest-job-first, and the shortest remaining processing time policy. For each of these policies, we first express the waiting-time distributions in terms of intervisit-time distributions. Next, we use these expressions to derive the asymptotic waiting-time distributions under heavy-traffic assumptions, i.e. when the system tends to saturate. The results show that in all cases the asymptotic waiting-time distribution at queueiis fully characterized and of the form Γ Θi, with Γ and Θiindependent, and where Γ is gamma distributed with known parameters (and the same for all scheduling policies). We derive the distribution of the random variable Θiwhich explicitly expresses the impact of the local service order on the asymptotic waiting-time distribution. The results provide new fundamental insight into the impact of the local scheduling policy on the performance of a general class of polling models. The asymptotic results suggest simple closed-form approximations for the complete waiting-time distributions for stable systems with arbitrary load values.

scholarly journals Polling models with renewal arrivals: A new method to derive heavy-traffic asymptotics

2007 ◽  
Vol 64 (9-12) ◽  
pp. 1029-1040 ◽  
Author(s):  
R.D. van der Mei ◽  
E.M.M. Winands
Keyword(s):  
Heavy Traffic ◽  
New Method ◽  
Polling Models

Heavy traffic analysis for continuous polling models

1997 ◽  
Vol 34 (03) ◽  
pp. 720-732 ◽  
Author(s):  
Dirk P. Kroese
Keyword(s):  
Steady State ◽  
Gamma Distribution ◽  
Branching Processes ◽  
Heavy Traffic ◽  
Traffic Analysis ◽  
Polling System ◽  
Polling Models ◽  
Heavy Traffic Analysis ◽  
Age Dependent ◽  
The Relationship

We consider a continuous polling system in heavy traffic. Using the relationship between such systems and age-dependent branching processes, we show that the steady-state number of waiting customers in heavy traffic has approximately a gamma distribution. Moreover, given their total number, the configuration of these customers is approximately deterministic.

scholarly journals Heavy-traffic limits for polling models with exhaustive service and non-FCFS service order policies

2015 ◽  
Vol 47 (4) ◽  
pp. 989-1014 ◽  
Author(s):  
P. Vis ◽  
R. Bekker ◽  
R. D. van der Mei
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Heavy Traffic ◽  
Processor Sharing ◽  
Waiting Time Distribution ◽  
Asymptotic Results ◽  
Local Service ◽  
Waiting Time Distributions ◽  
Polling Models ◽  
The Impact

We study cyclic polling models with exhaustive service at each queue under a variety of non-FCFS (first-come-first-served) local service orders, namely last-come-first-served with and without preemption, random-order-of-service, processor sharing, the multi-class priority scheduling with and without preemption, shortest-job-first, and the shortest remaining processing time policy. For each of these policies, we first express the waiting-time distributions in terms of intervisit-time distributions. Next, we use these expressions to derive the asymptotic waiting-time distributions under heavy-traffic assumptions, i.e. when the system tends to saturate. The results show that in all cases the asymptotic waiting-time distribution at queue i is fully characterized and of the form Γ Θi, with Γ and Θi independent, and where Γ is gamma distributed with known parameters (and the same for all scheduling policies). We derive the distribution of the random variable Θi which explicitly expresses the impact of the local service order on the asymptotic waiting-time distribution. The results provide new fundamental insight into the impact of the local scheduling policy on the performance of a general class of polling models. The asymptotic results suggest simple closed-form approximations for the complete waiting-time distributions for stable systems with arbitrary load values.

LIMIT THEOREMS FOR POLLING MODELS WITH INCREASING SETUPS

2001 ◽  
Vol 15 (1) ◽  
pp. 35-55 ◽  
Author(s):  
Tava Lennon Olsen
Keyword(s):  
Heavy Traffic ◽  
Random Variable ◽  
Setup Time ◽  
Setup Times ◽  
Single Server ◽  
Uniform Random Variable ◽  
Polling Models ◽  
Polling Model ◽  
Server Systems ◽  
The Mean

Multiclass single-server systems with significant setup times (polling models) are common in industry. This article considers asymptotics for polling models with increasing setup times. Two types of polling model are considered, namely (a) polling models with polling tables, exhaustive service, and deterministic setups, and (b) cyclic exhaustive service polling models with general setups under heavy traffic. It is shown that as the mean setup time increases to infinity, the scaled intervisit time for each queue (time between service of that queue) converges in probability to a constant. This, in turn, is shown to imply that scaled steady-state waiting time converges in distribution to either a uniform distribution or a simple discrete random variable multiplied by a uniform random variable as setups tend to infinity. These results lead to considerable insight into the behavior of systems with setups, and conclusions are drawn with respect to previous studies.

Heavy traffic analysis for continuous polling models

1997 ◽  
Vol 34 (3) ◽  
pp. 720-732 ◽  
Author(s):  
Dirk P. Kroese
Keyword(s):  
Steady State ◽  
Gamma Distribution ◽  
Branching Processes ◽  
Heavy Traffic ◽  
Traffic Analysis ◽  
Polling System ◽  
Polling Models ◽  
Heavy Traffic Analysis ◽  
Age Dependent ◽  
The Relationship

We consider a continuous polling system in heavy traffic. Using the relationship between such systems and age-dependent branching processes, we show that the steady-state number of waiting customers in heavy traffic has approximately a gamma distribution. Moreover, given their total number, the configuration of these customers is approximately deterministic.

Analisis Daya Dukung Tanah Dan Bahan Pondasi Tiang Pancang Pada Pembangunan Jembatan Kab. Jombang

2020 ◽  
Vol 9 (1) ◽  
pp. 32-37
Author(s):  
Ruslan Hidayat ◽  
Saiful Arfaah
Keyword(s):  
Carrying Capacity ◽  
Pile Foundation ◽  
Heavy Traffic ◽  
Traffic Volume ◽  
Material Strength ◽  
Cone Penetrometer ◽  
The Village

One of the most important factors in the structure of the pile foundation in the construction of the bridge is the carrying capacity of the soil so as not to collapse. Construction of a bridge in the village of Klitik in Jombang Regency to be built due to heavy traffic volume. The foundation plan to be used is a pile foundation with a diameter of 50 cm, the problem is what is the value of carrying capacity of soil and material. The equipment used is the Dutch Cone Penetrometer with a capacity of 2.50 tons with an Adhesion Jacket Cone. The detailed specifications of this sondir are as follows: Area conus 10 cm², piston area 10 cm², coat area 100 cm², as for the results obtained The carrying capacity of the soil is 60.00 tons for a diameter of 30 cm, 81,667 tons for a diameter of 35 cm, 106,667 tons for a diameter of 40 cm, 150,000 tons for a diameter of 50 cm for material strength of 54,00 tons for a diameter of 30 cm, 73,500 tons for a diameter of 35 cm, 96,00 tons for a diameter of 40 cm, 166,666 tons for a diameter of 50 cm

A Study on Job Satisfaction among Tamil Nadu State Transport Corporation (TNSTC) Employees at Tiruvarur Branch

GIS Business ◽  
2019 ◽  
Vol 14 (6) ◽  
pp. 230-242
Author(s):  
M. Ganesan, K ◽  
K. Veerakumar ◽  
N. R Vembu ◽  
Dr. M. K Durgamani ◽  
Dr. Renuka
Keyword(s):  
Job Satisfaction ◽  
Job Stress ◽  
Tamil Nadu ◽  
Heavy Traffic ◽  
Road Transportation ◽  
The Road ◽  
Tamil Nadu State ◽  
On The Road ◽  
Day By Day ◽  
Labour Turnover

Job satisfaction is an important factor for employees working in formal and informal sector. The job is small or big, permanent or temporary, risky or non-risky, job satisfaction is important. It is the mental feeling which drives the employees to excel. Job satisfaction is a combination of psychological, physiological and environmental circumstances. A satisfied employee is a contented and happy human being. The labour turnover depends upon job satisfaction. Even highly paid employees quit the job when they are not satisfied with the job. Road transportation in Tamilnadu is growing day by day. Job stress in the road transportation is very high due to increase in number of vehicle playing on the road and heavy traffic. The drivers and conductors working in public transport corporation are suffering from high job stress. If drivers and conductors are not satisfied with their job which leads to mental stresses and affects the productivity and also creates accidents. In this present study the researchers made an attempt to study the level of job satisfaction among the drivers and conductors who are working in the Tamilnadu State Transport Corporation (TNSTC). The study reveals the expectations of drivers and conductors working in TNSTC with regards to the attributes like salary, promotion and fringe benefits etc., are satisfactory and not detrimental. 

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