A two-level mixed service polling model with batch arrival

2015 ◽  
pp. 257-262
Keyword(s):  
Batch Arrival ◽  
Polling Model

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.

Some EATA properties for marked point processes

1995 ◽  
Vol 32 (04) ◽  
pp. 922-929
Author(s):  
D. Kofman ◽  
H. Korezlioglu
Keyword(s):  
Point Processes ◽  
Stochastic Integral ◽  
Marked Point ◽  
Marked Point Processes ◽  
Batch Arrival ◽  
Integral Approach ◽  
Arrival Processes

We derive an ESTA property for marked point processes similar to Wolff's PASTA property for ordinary (non-marked) point processes, via a stochastic integral approach. This new ESTA property allows us to extend a known result on the conditional PASTA property and to derive an ASTA property for batch arrival processes. We also present an application of our results.

Analysis of an Asymmetric Polling Model with Cycle-time Constraint

1991 ◽  
pp. 493-508 ◽  
Author(s):  
Kazuta Nakamura ◽  
Tetsuya Takine ◽  
Yutaka Takahashi ◽  
Toshiharu Hasegawa
Keyword(s):  
Cycle Time ◽  
Time Constraint ◽  
Polling Model

THE MX/D/c BATCH ARRIVAL QUEUE

2005 ◽  
Vol 19 (3) ◽  
pp. 345-349 ◽  
Author(s):  
Geert Jan Franx
Keyword(s):  
Explicit Expression ◽  
Waiting Time ◽  
Probabilistic Analysis ◽  
Generating Functions ◽  
Time Distribution ◽  
Laplace Transforms ◽  
Batch Arrival ◽  
Waiting Time Distribution

A surprisingly simple and explicit expression for the waiting time distribution of the MX/D/c batch arrival queue is derived by a full probabilistic analysis, requiring neither generating functions nor Laplace transforms. Unlike the solutions known so far, this expression presents no numerical complications, not even for high traffic intensities.

scholarly journals M/G/∞ POLLING SYSTEMS WITH RANDOM VISIT TIMES

2007 ◽  
Vol 22 (1) ◽  
pp. 81-106 ◽  
Author(s):  
M. Vlasiou ◽  
U. Yechiali
Keyword(s):  
Service Time ◽  
Probability Generating Function ◽  
Expected Value ◽  
Polling Systems ◽  
Service Time Distribution ◽  
Polling System ◽  
Stieltjes Transform ◽  
Polling Model ◽  
Queue Lengths ◽  
Number Of Customers

We consider a polling system where a group of an infinite number of servers visits sequentially a set of queues. When visited, each queue is attended for a random time. Arrivals at each queue follow a Poisson process, and the service time of each individual customer is drawn from a general probability distribution function. Thus, each of the queues comprising the system is, in isolation, anM/G/∞-type queue. A job that is not completed during a visit will have a new service-time requirement sampled from the service-time distribution of the corresponding queue. To the best of our knowledge, this article is the first in which anM/G/∞-type polling system is analyzed. For this polling model, we derive the probability generating function and expected value of the queue lengths and the Laplace–Stieltjes transform and expected value of the sojourn time of a customer. Moreover, we identify the policy that maximizes the throughput of the system per cycle and conclude that under the Hamiltonian-tour approach, the optimal visiting order isindependentof the number of customers present at the various queues at the start of the cycle.

A batch arrival queue with impatient customers

2014 ◽  
Vol 42 (2) ◽  
pp. 180-185 ◽  
Author(s):  
Bara Kim ◽  
Jeongsim Kim
Keyword(s):  
Batch Arrival ◽  
Impatient Customers
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