Setups in polling models: does it make sense to set up if no work is waiting?

1999 ◽  
Vol 36 (2) ◽  
pp. 585-592 ◽  
Author(s):  
Robert B. Cooper ◽  
Shun-Chen Niu ◽  
Mandyam M. Srinivasan
Keyword(s):  
Waiting Times ◽  
Setup Times ◽  
Service Time Distribution ◽  
Polling Models ◽  
Polling Model ◽  
State Dependent ◽  
Switchover Times ◽  
The Difference ◽  
Set Up ◽  
Better Than

We compare two versions of a symmetric two-queue polling model with switchover times and setup times. The SI version has State-Independent setups, according to which the server sets up at the polled queue whether or not work is waiting there; and the SD version has State-Dependent setups, according to which the server sets up only when work is waiting at the polled queue. Naive intuition would lead one to believe that the SD version should perform better than the SI version. We characterize the difference in the expected waiting times of these two versions, and we uncover some surprising facts. In particular, we show that, regardless of the server utilization or the service-time distribution, the SD version performs (i) the same as, (ii) worse than, or (iii) better than its SI counterpart if the switchover and setup times are, respectively, (i) both constants, (ii) variable (i.e. non-deterministic) and constant, or (iii) constant and variable. Only (iii) is consistent with naive intuition.

Setups in polling models: does it make sense to set up if no work is waiting?

1999 ◽  
Vol 36 (02) ◽  
pp. 585-592 ◽  
Author(s):  
Robert B. Cooper ◽  
Shun-Chen Niu ◽  
Mandyam M. Srinivasan
Keyword(s):  
Waiting Times ◽  
Setup Times ◽  
Service Time Distribution ◽  
Polling Models ◽  
Polling Model ◽  
State Dependent ◽  
Switchover Times ◽  
The Difference ◽  
Set Up ◽  
Better Than

We compare two versions of a symmetric two-queue polling model with switchover times and setup times. The SI version has State-Independent setups, according to which the server sets up at the polled queue whether or not work is waiting there; and the SD version has State-Dependent setups, according to which the server sets up only when work is waiting at the polled queue. Naive intuition would lead one to believe that the SD version should perform better than the SI version. We characterize the difference in the expected waiting times of these two versions, and we uncover some surprising facts. In particular, we show that, regardless of the server utilization or the service-time distribution, the SD version performs (i) the same as, (ii) worse than, or (iii) better than its SI counterpart if the switchover and setup times are, respectively, (i) both constants, (ii) variable (i.e. non-deterministic) and constant, or (iii) constant and variable. Only (iii) is consistent with naive intuition.

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.

Comparison results for M/G/1 queues with waiting and sojourn time deadlines

2019 ◽  
Vol 56 (2) ◽  
pp. 524-532 ◽  
Author(s):  
Yoshiaki Inoue
Keyword(s):  
Performance Measures ◽  
Time Distribution ◽  
Waiting Times ◽  
Loss Probability ◽  
The Other ◽  
Service Time Distribution ◽  
Impatient Customers ◽  
Comparison Results ◽  
New Better Than Used ◽  
Better Than

AbstractThis paper considers two variants of M/G/1 queues with impatient customers, which are denoted by M/G/1+Gw and M/G/1+Gs. In the M/G/1+Gw queue customers have deadlines for their waiting times, and they leave the system immediately if their services do not start before the expiration of their deadlines. On the other hand, in the M/G/1+Gs queue customers have deadlines for their sojourn times, where customers in service also immediately leave the system when their deadlines expire. In this paper we derive comparison results for performance measures of these models. In particular, we show that if the service time distribution is new better than used in expectation, then the loss probability in the M/G/1+Gs queue is greater than that in the M/G/1+Gw queue.

scholarly journals WAIT-AND-SEE STRATEGIES IN POLLING MODELS

2011 ◽  
Vol 26 (1) ◽  
pp. 17-42 ◽  
Author(s):  
Frank Aurzada ◽  
Sergej Beck ◽  
Michael Scheutzow
Keyword(s):  
Lower Bound ◽  
Cyclic Order ◽  
General Distribution ◽  
New Work ◽  
Queuing Delay ◽  
Polling Models ◽  
Polling Model ◽  
Switchover Times ◽  
Wait And See ◽  
Service Times

We consider a general polling model with N stations. The stations are served exhaustively and in cyclic order. Once a station queue falls empty, the server does not immediately switch to the next station. Rather, it waits at the station for the possible arrival of new work (“wait-and-see”) and, in the case of this happening, it restarts service in an exhaustive fashion. The total time the server waits idly is set to be a fixed, deterministic parameter for each station. Switchover times and service times are allowed to follow some general distribution, respectively. In some cases, which can be characterized, this strategy yields a strictly lower average queuing delay than for the exhaustive strategy, which corresponds to setting the “wait-and-see credit” equal to zero for all stations. This extends the results of Peköz [12] and of Boxma et al. [4]. Furthermore, we give a lower bound for the delay for all strategies that allow the server to wait at the stations even though no work is present.

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.

Removal of inelastically scattered electrons substantially increases phase contrast on frozen-hydrated molecules

1987 ◽  
Vol 45 ◽  
pp. 652-653
Author(s):  
John P. Langmore ◽  
Brian D. Athey
Keyword(s):  
Electron Diffraction ◽  
Phase Contrast ◽  
Low Dose ◽  
Dark Field ◽  
Biological Structure ◽  
Bright Field ◽  
Low Contrast ◽  
Negative Stain ◽  
The Difference ◽  
Better Than

Although electron diffraction indicates better than 0.3nm preservation of biological structure in vitreous ice, the imaging of molecules in ice is limited by low contrast. Thus, low-dose images of frozen-hydrated molecules have significantly more noise than images of air-dried or negatively-stained molecules. We have addressed the question of the origins of this loss of contrast. One unavoidable effect is the reduction in scattering contrast between a molecule and the background. In effect, the difference in scattering power between a molecule and its background is 2-5 times less in a layer of ice than in vacuum or negative stain. A second, previously unrecognized, effect is the large, incoherent background of inelastic scattering from the ice. This background reduces both scattering and phase contrast by an additional factor of about 3, as shown in this paper. We have used energy filtration on the Zeiss EM902 in order to eliminate this second effect, and also increase scattering contrast in bright-field and dark-field.

PENERAPAN MODEL PEMBELAJARAN KOOPERATIF TIPE STAD DENGAN PENDEKATAN RME UNTUK MENINGKATKAN HASIL BELAJAR MATEMATIKA SISWA KELAS IX SMP MUHAMMADIYAH PADANG LUAS KECAMATAN TAMBANG KABUPATEN KAMPAR

2018 ◽  
Vol 2 (5) ◽  
pp. 744
Author(s):  
Zainur Zainur
Keyword(s):  
Action Research ◽  
Cooperative Learning ◽  
Student Learning ◽  
Learning Outcomes ◽  
Mathematics Learning ◽  
Student Learning Outcomes ◽  
Learning Model ◽  
Research Instrument ◽  
The Difference ◽  
Better Than

This research was motivated by the low learning outcomes of grade IX SMP Muhammadiyah Padang LuasKecamatan Tambang Kabupaten Kampar. This study aims to improve learning outcomes in mathematicslearning through STAD type cooperative learning with the RME approach in class IX SMP MuhammadiyahPadang Luas Kecamatan Tambang Kabupaten Kampar. The subjects of this study were all classes IX in SMPMuhammadiyah Padang Luas Kecamatan Tambang Kabupaten Kampar totaling 26 people. The form ofresearch is classroom action research. This research instrument consists of performance instruments and datacollection instruments in the form of teacher activity observation sheets and activities. The results of the studystated that there were significant differences between students' mathematics learning outcomes before applyingthe STAD type cooperative learning model with the RME approach with after applying the STAD typecooperative learning model with the RME approach. The difference shows student learning outcomes after theaction is better than before the action with completeness reaching 80.77% or 21 completed. Based on the resultsof the study and discussion it can be concluded that the application of STAD type learning model with RealisticMathematic Education (RME) approach can improve the learning outcomes of grade IX students of SMPMuhammadiyah Padang Luas Kecamatan Tambang Kabupaten Kampar on statistical material.

Determination of trace concentrations of copper by FIA-FAAS after preconcentration on chelating sorbents

1989 ◽  
Vol 54 (7) ◽  
pp. 1785-1794 ◽  
Author(s):  
Vlastimil Kubáň ◽  
Josef Komárek ◽  
Zbyněk Zdráhal
Keyword(s):  
Sampling Frequency ◽  
Copper Determination ◽  
Flow Rates ◽  
Sample Injection ◽  
Injection Flow ◽  
Chelating Sorbents ◽  
Set Up ◽  
Trace Concentrations ◽  
Better Than

A FIA-FAAS apparatus containing a six-channel sorption equipment with five 3 x 26 mm microcolumns packed with Spheron Oxin 1 000, Ostsorb Oxin and Ostsorb DTTA was set up. Combined with sorption from 0.002M acetate buffer at pH 4.2 and desorption with 2M-HCl, copper can be determined at concentrations up to 100, 150 and 200 μg l-1, respectively. For sample and eluent flow rates of 5.0 and 4.0 ml min-1, respectively, and a sample injection time of 5 min, the limit of copper determination is LQ = 0.3 μg l-1, repeatability sr is better than 2% and recovery is R = 100 ± 2%. The enrichment factor is on the order of 102 and is a linear function of time (volume) of sample injection up to 5 min and of the sample injection flow rate up to 11 ml min-1 for Spheron Oxin 1 000 and Ostsorb DTTA. For times of sorption of 60 and 300 s, the sampling frequency is 70 and 35 samples/h, respectively. The parameters of the FIA-FAAS determination (acetylene-air flame) are comparable to or better than those achieved by ETA AAS. The method was applied to the determination of traces of copper in high-purity water.

Analysis of Single Buffer Random Polling System With State-Dependent Input Process and Server/Station Breakdowns

2018 ◽  
Vol 9 (1) ◽  
pp. 22-50 ◽  
Author(s):  
Thomas Y.S. Lee
Keyword(s):  
Steady State ◽  
Linear Model ◽  
Repair Process ◽  
Polling System ◽  
Steady State Analysis ◽  
Relaxation System ◽  
Polling Model ◽  
State Dependent ◽  
Non Linear ◽  
State Analysis

Models and analytical techniques are developed to evaluate the performance of two variations of single buffers (conventional and buffer relaxation system) multiple queues system. In the conventional system, each queue can have at most one customer at any time and newly arriving customers find the buffer full are lost. In the buffer relaxation system, the queue being served may have two customers, while each of the other queues may have at most one customer. Thomas Y.S. Lee developed a state-dependent non-linear model of uncertainty for analyzing a random polling system with server breakdown/repair, multi-phase service, correlated input processes, and single buffers. The state-dependent non-linear model of uncertainty introduced in this paper allows us to incorporate correlated arrival processes where the customer arrival rate depends on the location of the server and/or the server's mode of operation into the polling model. The author allows the possibility that the server is unreliable. Specifically, when the server visits a queue, Lee assumes that the system is subject to two types of failures: queue-dependent, and general. General failures are observed upon server arrival at a queue. But there are two possibilities that a queue-dependent breakdown (if occurs) can be observed; (i) is observed immediately when it occurs and (ii) is observed only at the end of the current service. In both cases, a repair process is initiated immediately after the queue-dependent breakdown is observed. The author's model allows the possibility of the server breakdowns/repair process to be non-stationary in the number of breakdowns/repairs to reflect that breakdowns/repairs or customer processing may be progressively easier or harder, or that they follow a more general learning curve. Thomas Y.S. Lee will show that his model encompasses a variety of examples. He was able to perform both transient and steady state analysis. The steady state analysis allows us to compute several performance measures including the average customer waiting time, loss probability, throughput and mean cycle time.

Experimental Investigation into Driver Behavior along Curved and Parallel Diverging Terminals of Exit Interchange Ramps

2021 ◽  
pp. 036119812199742
Author(s):  
Alberto Portera ◽  
Marco Bassani
Keyword(s):  
Design Stage ◽  
Lane Change ◽  
Age And Gender ◽  
Traffic Conditions ◽  
Current Design ◽  
The Difference ◽  
Safety Countermeasures ◽  
And Gender ◽  
Set Up ◽  
Curve Radius

Current design manuals provide guidance on how to design exit ramps to facilitate driving operations and minimize the incidence of crashes. They also suggest that interchanges should be built along straight roadway sections. These criteria may prove ineffective in situations where there is no alternative to terminals being located along curved motorway segments. The paper investigates driving behavior along parallel deceleration curved terminals, with attention paid to the difference in impact between terminals having a curvature which is the same sign as the motorway segment (i.e., continue design), and those having an opposite curvature (i.e., reverse design). A driving simulation study was set up to collect longitudinal and transversal driver behavioral data in response to experimental factor variations. Forty-eight drivers were stratified on the basis of age and gender, and asked to drive along three randomly assigned circuits with off-ramps obtained by combining experimental factors such as motorway mainline curve radius (2 values), terminal length (3), curve direction (2), and traffic conditions (2). The motorway radius was found to be significant for drivers’ preferred speed when approaching the terminal. Terminal length and traffic volume do not have a significant impact on either longitudinal or transversal driver outputs. However, the effect of curve direction was found to be significant, notably for reverse terminals which do not compel drivers to select appropriate speeds and lane change positions. This terminal type can give rise to critical driving situations that should be considered at the design stage to facilitate the adoption of appropriate safety countermeasures.

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