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.

Analysis of the M x/G/1 queue by N-policy and multiple vacations

1994 ◽  
Vol 31 (02) ◽  
pp. 476-496
Author(s):  
Ho Woo Lee ◽  
Soon Seok Lee ◽  
Jeong Ok Park ◽  
K. C. Chae
Keyword(s):  
Performance Measures ◽  
Queue Length ◽  
Time Distribution ◽  
Queueing System ◽  
Random Variables ◽  
System Size ◽  
The Other ◽  
Waiting Time Distribution ◽  
Multiple Vacations ◽  
Linear Cost

We consider an Mx /G/1 queueing system with N-policy and multiple vacations. As soon as the system empties, the server leaves for a vacation of random length V. When he returns, if the queue length is greater than or equal to a predetermined value N(threshold), the server immediately begins to serve the customers. If he finds less than N customers, he leaves for another vacation and so on until he finally finds at least N customers. We obtain the system size distribution and show that the system size decomposes into three random variables one of which is the system size of ordinary Mx /G/1 queue. The interpretation of the other random variables will be provided. We also derive the queue waiting time distribution and other performance measures. Finally we derive a condition under which the optimal stationary operating policy is achieved under a linear cost structure.

scholarly journals Cyclic queueing networks with subexponential service times

2004 ◽  
Vol 41 (03) ◽  
pp. 791-801
Author(s):  
H. Ayhan ◽  
Z. Palmowski ◽  
S. Schlegel
Keyword(s):  
Queueing Networks ◽  
Time Distribution ◽  
Waiting Times ◽  
Queueing Network ◽  
Service Time Distribution ◽  
Tail Behavior ◽  
Cycle Times ◽  
General Service Times ◽  
Service Times ◽  
General Service

For a K-stage cyclic queueing network with N customers and general service times, we provide bounds on the nth departure time from each stage. Furthermore, we analyze the asymptotic tail behavior of cycle times and waiting times given that at least one service-time distribution is subexponential.

Analysis and Experimentation of Multi-S Rotors for Vertical Wind Turbine Applications

2012 ◽  
Vol 260-261 ◽  
pp. 97-102
Author(s):  
E.M. ElBeheiry ◽  
W.A. El-Askary
Keyword(s):  
Performance Measures ◽  
Power Factor ◽  
Design Parameter ◽  
The Other ◽  
Experimental Investigations ◽  
Speed Ratio ◽  
Performance Potentials ◽  
Remarkable Deviation ◽  
Theoretical Performance ◽  
Better Than

This article presents a new, multi-foil-blades (multi-S) rotor and compare its performance potentials with traditional (Single-S) Savomius rotor . Theoretical and experimental investigations show that the performance of the multi-S rotor is better than the other classical designs of Savonius rotor in terms of the resulting power factor. Analytical equations for power and torque factors are developed for both the single- and multi-S rotors with ideal flow assumed. These equations are proven very effective in describing the performance potentials of these rotors for a range of speed ratio less than or equals 0.7. This result is experimentally justified for both types of rotors. For speed ratios higher than 0.7, a remarkable deviation occurs between the theoretical performance measures provided by the developed equations and the experimentally measured ones. A geometric design parameter which depends on the internal construction of the proposed multi-S rotor is found to be of great impact on the attained power factor. A power factor for the multi-S rotor can be much more than that of a single-S one having the same height and outer size according to the chosen values of this design parameter.

M/Ck/1 Queue with Impatient Customers

2016 ◽  
pp. 22-37
Author(s):  
Umay Uzunoglu Kocer
Keyword(s):  
Service Time ◽  
Time Distribution ◽  
Random Variable ◽  
Death Process ◽  
Single Server ◽  
Service Time Distribution ◽  
Birth And Death Process ◽  
Impatient Customers ◽  
Constant Rate ◽  
Long Time

A single-server queuing system with impatient customers and Coxian service is examined. It is assumed that arrivals are Poisson with a constant rate. When the server is busy upon an arrival, customer joins the queue and there is an infinite capacity of the queue. Since the variance of the service time is relatively high, the service time distribution is characterized by k-phase Cox distribution. Due to the high variability of service times and since some of the services take extremely long time, customers not only in the queue, but also in the service may become impatient. Each customer, upon arrival, activates an individual timer and starts his patience time. The patience time for each customer is a random variable which has exponential distribution. If the service does not completed before the customer's time expires, the customer abandons the queue never to return. The model is expressed as birth-and-death process and the balance equations are provided.

New better than used processes

1983 ◽  
Vol 15 (3) ◽  
pp. 601-615 ◽  
Author(s):  
Albert W. Marshall ◽  
Moshe Shared
Keyword(s):  
First Passage Time ◽  
Waiting Times ◽  
Random Variables ◽  
Passage Time ◽  
Renewal Processes ◽  
Recovery Processes ◽  
Strong Markov ◽  
New Better Than Used ◽  
Better Than ◽  
Quantities Of Interest

A stochastic process , such that P{Z(0) = 0} = 1, is said to be new better than used (NBU) if, for every x, the first-passage time Tx = inf {t: Z(t) > x} satisfies P{TX > s + t} for everys . In this paper it is shown that many useful processes are NBU. Examples of such processes include processes with shocks and recovery, processes with random repair-times, various Gaver–Miller processes and some strong Markov processes. Applications in reliability theory, queueing, dams, inventory and electrical activity of neurons are indicated. It is shown that various waiting times for clusters of events and for short and wide gaps in some renewal processes are NBU random variables. The NBU property of processes and random variables can be used to obtain bounds on various probabilistic quantities of interest; this is illustrated numerically.

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 M/G/1/K system with push-out scheme under vacation policy

1996 ◽  
Vol 9 (2) ◽  
pp. 143-157 ◽  
Author(s):  
Shoji Kasahara ◽  
Hideaki Takagi ◽  
Yutaka Takahashi ◽  
Toshiharu Hasegawa
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Waiting Times ◽  
Numerical Results ◽  
The Other ◽  
Waiting Time Distribution ◽  
Stieltjes Transform ◽  
Multiple Vacations ◽  
Push Out

We consider an M/G/1/K system with push-out scheme and multiple vacations. This model is particularly important in situations where it is essential to provide short waiting times to messages which are selected for service. We analyze the behavior of two types of messages: one that succeeds in transmission and the other that fails. We derive the Laplace-Stieltjes transform of the waiting time distribution for the message which is eventually served. Finally, we show some numerical results including the comparisons between the push-out and the ordinary blocking models.

Analysis of the Mx/G/1 queue by N-policy and multiple vacations

1994 ◽  
Vol 31 (2) ◽  
pp. 476-496 ◽  
Author(s):  
Ho Woo Lee ◽  
Soon Seok Lee ◽  
Jeong Ok Park ◽  
K. C. Chae
Keyword(s):  
Performance Measures ◽  
Queue Length ◽  
Time Distribution ◽  
Queueing System ◽  
Random Variables ◽  
System Size ◽  
The Other ◽  
Waiting Time Distribution ◽  
Multiple Vacations ◽  
Linear Cost

We consider an Mx/G/1 queueing system with N-policy and multiple vacations. As soon as the system empties, the server leaves for a vacation of random length V. When he returns, if the queue length is greater than or equal to a predetermined value N(threshold), the server immediately begins to serve the customers. If he finds less than N customers, he leaves for another vacation and so on until he finally finds at least N customers. We obtain the system size distribution and show that the system size decomposes into three random variables one of which is the system size of ordinary Mx/G/1 queue. The interpretation of the other random variables will be provided. We also derive the queue waiting time distribution and other performance measures. Finally we derive a condition under which the optimal stationary operating policy is achieved under a linear cost structure.

scholarly journals Cyclic queueing networks with subexponential service times

2004 ◽  
Vol 41 (3) ◽  
pp. 791-801 ◽  
Author(s):  
H. Ayhan ◽  
Z. Palmowski ◽  
S. Schlegel
Keyword(s):  
Queueing Networks ◽  
Time Distribution ◽  
Waiting Times ◽  
Queueing Network ◽  
Service Time Distribution ◽  
Tail Behavior ◽  
Cycle Times ◽  
General Service Times ◽  
Service Times ◽  
General Service

For a K-stage cyclic queueing network with N customers and general service times, we provide bounds on the nth departure time from each stage. Furthermore, we analyze the asymptotic tail behavior of cycle times and waiting times given that at least one service-time distribution is subexponential.

scholarly journals Bounds of the stationary distribution in M/G/1 retrial queue with two-way communication and n types of outgoing calls

2019 ◽  
Vol 29 (3) ◽  
pp. 375-391
Author(s):  
Lala Alem ◽  
Mohamed Boualem ◽  
Djamil Aissani
Keyword(s):  
Markov Chain ◽  
Stationary Distribution ◽  
Performance Measures ◽  
Time Distribution ◽  
Retrial Queue ◽  
Main Idea ◽  
Embedded Markov Chain ◽  
Stochastic Comparison ◽  
Service Time Distribution ◽  
Comparison Approach

In this article we analyze the M=G=1 retrial queue with two-way communication and n types of outgoing calls from a stochastic comparison viewpoint. The main idea is that given a complex Markov chain that cannot be analyzed numerically, we propose to bound it by a new Markov chain, which is easier to solve by using a stochastic comparison approach. Particularly, we study the monotonicity of the transition operator of the embedded Markov chain relative to the stochastic and convex orderings. Bounds are also obtained for the stationary distribution of the embedded Markov chain at departure epochs. Additionally, the performance measures of the considered system can be estimated by those of an M=M=1 retrial queue with two-way communication and n types of outgoing calls when the service time distribution is NBUE (respectively, NWUE). Finally, we test numerically the accuracy of the proposed bounds.

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