A Decomposition Theorem for Polling Models: The Switchover Times are Effectively Additive

1996 ◽  
Vol 44 (4) ◽  
pp. 629-633 ◽  
Author(s):  
Robert B. Cooper ◽  
Shun-Chen Niu ◽  
Mandyam M. Srinivasan
Keyword(s):  
Decomposition Theorem ◽  
Polling Models ◽  
Switchover Times

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.

scholarly journals Polling Models With and Without Switchover Times

1997 ◽  
Vol 45 (4) ◽  
pp. 536-543 ◽  
Author(s):  
S. C. Borst ◽  
O. J. Boxma
Keyword(s):  
Polling Models ◽  
Switchover Times

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.

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 Relating polling models with zero and nonzero switchover times

1995 ◽  
Vol 19 (1-2) ◽  
pp. 149-168 ◽  
Author(s):  
Mandyam M. Srinivasan ◽  
Shun-Chen Niu ◽  
Robert B. Cooper
Keyword(s):  
Polling Models ◽  
Switchover Times

scholarly journals Polynomial identities related to special Schubert varieties

2021 ◽  
Author(s):  
Francesca Cioffi ◽  
Davide Franco ◽  
Carmine Sessa
Keyword(s):  
Arbitrary Number ◽  
Schubert Variety ◽  
Decomposition Theorem ◽  
Point Of View ◽  
Explicit Description ◽  
Intersection Cohomology ◽  
Schubert Varieties ◽  
Polynomial Identities ◽  
Poincaré Polynomial

AbstractLet $$\mathcal S$$ S be a single condition Schubert variety with an arbitrary number of strata. Recently, an explicit description of the summands involved in the decomposition theorem applied to such a variety has been obtained in a paper of the second author. Starting from this result, we provide an explicit description of the Poincaré polynomial of the intersection cohomology of $$\mathcal S$$ S by means of the Poincaré polynomials of its strata, obtaining interesting polynomial identities relating Poincaré polynomials of several Grassmannians, both by a local and by a global point of view. We also present a symbolic study of a particular case of these identities.

scholarly journals Curvature of quaternionic Kähler manifolds with $$S^1$$-symmetry

2021 ◽  
Author(s):  
V. Cortés ◽  
A. Saha ◽  
D. Thung
Keyword(s):  
Curvature Tensor ◽  
Decomposition Theorem ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Riemann Curvature ◽  
Riemann Curvature Tensor ◽  
Cohomogeneity One ◽  
Civita Connection ◽  
Levi Civita Connection ◽  
Quaternionic Kähler

AbstractWe study the behavior of connections and curvature under the HK/QK correspondence, proving simple formulae expressing the Levi-Civita connection and Riemann curvature tensor on the quaternionic Kähler side in terms of the initial hyper-Kähler data. Our curvature formula refines a well-known decomposition theorem due to Alekseevsky. As an application, we compute the norm of the curvature tensor for a series of complete quaternionic Kähler manifolds arising from flat hyper-Kähler manifolds. We use this to deduce that these manifolds are of cohomogeneity one.

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