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 (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.

A service model in which the server is required to search for customers

1984 ◽  
Vol 21 (1) ◽  
pp. 157-166 ◽  
Author(s):  
Marcel F. Neuts ◽  
M. F. Ramalhoto
Keyword(s):  
Poisson Process ◽  
Numerical Computation ◽  
Probability Distributions ◽  
General Distribution ◽  
Search Process ◽  
Single Server ◽  
Stationary Probability ◽  
Service Model ◽  
Service Times ◽  
Number Of Customers

Customers enter a pool according to a Poisson process and wait there to be found and processed by a single server. The service times of successive items are independent and have a common general distribution. Successive services are separated by seek phases during which the server searches for the next customer. The search process is Markovian and the probability of locating a customer in (t, t + dt) is proportional to the number of customers in the pool at time t. Various stationary probability distributions for this model are obtained in explicit forms well-suited for numerical computation.Under the assumption of exponential service times, corresponding results are obtained for the case where customers may escape from the pool.

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

scholarly journals Discrete- Time Queueing Model Geox/G/ꚙ with Bulk Arrival Rule

2020 ◽  
Vol 9 (3) ◽  
pp. 2585-2589
Keyword(s):  
Discrete Time ◽  
Geometric Distribution ◽  
Transient State ◽  
State Solution ◽  
General Distribution ◽  
Queueing Model ◽  
Service Times ◽  
Bulk Arrival ◽  
Number Of Customers

A discrete time queueing model is considered to estimate of the number of customers in the system. The arrivals, which are in groups of size X, inter-arrivals times and service times are distributed independent. The inter-arrivals fallows geometric distribution with parameter p and service times follows general distribution with parameter µ, we have derive the various transient state solution along with their moments and numerical illustrations in this paper.

Basic analysis of a head-of-the-line priority queue with renewal type input

1975 ◽  
Vol 12 (2) ◽  
pp. 346-352
Author(s):  
R. Schassberger
Keyword(s):  
Distribution Function ◽  
Priority Queue ◽  
General Distribution ◽  
Single Server ◽  
Service Times

A single server is fed by a renewal stream of individual customers. These are of type k with probability πk, k = 1, …, N, and are all served individually. Upon completion of a service the server proceeds immediately with a customer of the lowest type (= highest priority) present, if any. Service times for type k are drawn from a general distribution function Bk(t) concentrated on (0, ∞).We lay the foundations for a broad analysis of the model.

scholarly journals The stationary local sojourn time in single server tandem queues with renewal input

1999 ◽  
Vol 12 (4) ◽  
pp. 417-428
Author(s):  
Pierre Le Gall
Keyword(s):  
Sojourn Time ◽  
Stationary Regime ◽  
General Distribution ◽  
Single Server ◽  
Tandem Queues ◽  
Tandem Queue ◽  
Service Times

We start from an earlier paper evaluating the overall sojourn time to derive the local sojourn time in stationary regime, in a single server tandem queue of (m+1) stages with renewal input. The successive service times of a customer may or may not be mutually dependent, and are governed by a general distribution which may be different at each sage.

A service model in which the server is required to search for customers

1984 ◽  
Vol 21 (01) ◽  
pp. 157-166 ◽  
Author(s):  
Marcel F. Neuts ◽  
M. F. Ramalhoto
Keyword(s):  
Poisson Process ◽  
Numerical Computation ◽  
Probability Distributions ◽  
General Distribution ◽  
Search Process ◽  
Single Server ◽  
Stationary Probability ◽  
Service Model ◽  
Service Times ◽  
Number Of Customers

Customers enter a pool according to a Poisson process and wait there to be found and processed by a single server. The service times of successive items are independent and have a common general distribution. Successive services are separated by seek phases during which the server searches for the next customer. The search process is Markovian and the probability of locating a customer in (t, t + dt) is proportional to the number of customers in the pool at time t. Various stationary probability distributions for this model are obtained in explicit forms well-suited for numerical computation. Under the assumption of exponential service times, corresponding results are obtained for the case where customers may escape from the pool.

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 Retrial queues with recurrent demand option

1996 ◽  
Vol 9 (2) ◽  
pp. 221-228 ◽  
Author(s):  
K. Farahmand ◽  
N. H. Smith
Keyword(s):  
Poisson Process ◽  
Queueing System ◽  
Service System ◽  
Queueing Systems ◽  
Retrial Queues ◽  
General Distribution ◽  
Fixed Rate ◽  
Service Times ◽  
Request Service

The object of this paper is to analyze the model of a queueing system in which customers can call in only to request service: if the server is free, the customer enters service immediately. Otherwise, if the service system is occupied, the customer joins a source of unsatisfied customers called the orbit. On completion of each service the recipient of service has an option of leaving the system completely with probability 1−p or returning to the orbit with probability p. We consider two models characterized by the discipline governing the order of rerequests for service from the orbit. First, all the customers from the orbit apply at a fixed rate. Secondly, customers from the orbit are discouraged and reduce their rate of demand as more customers join the orbit. The arrival at and the demands from the orbit are both assumed to be according to the Poisson process. However, the service times for both primary customers and customers from the orbit are assumed to have a general distribution. We calculate several characteristic quantities of these queueing systems.

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