scholarly journals The Geo/Geo/1+1 Queueing System with Negative Customers

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Zhanyou Ma ◽  
Yalin Guo ◽  
Pengcheng Wang ◽  
Yumei Hou
Keyword(s):  
Performance Measures ◽  
Waiting Time ◽  
System Performance ◽  
Queue Length ◽  
Solution Method ◽  
Queueing System ◽  
Negative Customers ◽  
Idle Period ◽  
Matrix Geometric Solution ◽  
Qbd Process

We study a Geo/Geo/1+1 queueing system with geometrical arrivals of both positive and negative customers in which killing strategies considered are removal of customers at the head (RCH) and removal of customers at the end (RCE). Using quasi-birth-death (QBD) process and matrix-geometric solution method, we obtain the stationary distribution of the queue length, the average waiting time of a new arrival customer, and the probabilities of servers in busy or idle period, respectively. Finally, we analyze the effect of some related parameters on the system performance measures.

scholarly journals On the GI/M/1 Queue with Vacations and Multiple Service Phases

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Jianjun Li ◽  
Liwei Liu
Keyword(s):  
Performance Measures ◽  
Waiting Time ◽  
Solution Method ◽  
System Size ◽  
Mean Waiting Time ◽  
The Matrix ◽  
Matrix Geometric Solution ◽  
Semi Markov Process ◽  
Stationary Waiting Time ◽  
Number Of Customers

This paper considers a GI/M/1 queue with vacations and multiple service phases. Whenever the system becomes empty, the server takes a vacation, causing the system to move to vacation phase 0. If the server returns from a vacation to find no customer waiting, another vacation begins. Otherwise, the system jumps from phase 0 to some service phase i with probability qi,  i=1,2,…,N. Using the matrix geometric solution method and semi-Markov process, we obtain the distributions of the stationary system size at both arrival and arbitrary epochs. The distribution of the stationary waiting time of an arbitrary customer is also derived. In addition, we present some performance measures such as mean waiting time of an arbitrary customer, mean length of the type-i cycle, and mean number of customers in the system at the end of phase 0. Finally, some numerical examples are presented.

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 Operational behavior of the MAP/G/1 queue under N-policy with a single vacation and set-up

2002 ◽  
Vol 15 (2) ◽  
pp. 151-180
Author(s):  
Ho Woo Lee ◽  
Boo Yong Ahn
Keyword(s):  
Performance Measures ◽  
Waiting Time ◽  
Generating Functions ◽  
Queue Length ◽  
Stieltjes Transform ◽  
Arbitrary Time ◽  
Single Vacation ◽  
Set Up ◽  
Computation Algorithms

This paper considers the MAP/G/1 queue under N-policy with a single vacation and set-up. We derive the vector generating functions of the queue length at an arbitrary time and at departures in decomposed forms. We also derive the Laplace-Stieltjes transform of the waiting time. Computation algorithms for mean performance measures are provided.

Numerical solution for the performance characteristics of the M/M/C/K retrial queue with negative customers and exponential abandonments by using value extrapolation method

2019 ◽  
Vol 53 (3) ◽  
pp. 767-786
Author(s):  
Zidani Nesrine ◽  
Pierre Spiteri ◽  
Natalia Djellab
Keyword(s):  
System Performance ◽  
Algebraic System ◽  
Queueing System ◽  
Retrial Queue ◽  
Practical Interest ◽  
Extrapolation Method ◽  
Negative Customers ◽  
Multiprocessor Computer ◽  
Retrial Queueing System ◽  
Retrial Queueing

This paper deals with a retrial queueing system M/M/C/K with exponential abandonment at which positive and negative primary customers arrive according to Poisson processes. This model is of practical interest: it permits to analyze the performance in call centers or multiprocessor computer systems. For model under study, we find the ergodicity condition and also the approximate solution by applying Value Extrapolation method which includes solving of some algebraic system of equations. To this end, we have resolved the algebraic system in question by different numerical methods. We present also numerical results to analyze the system performance.

A note on the convexity of performance measures of M/M/c queueing systems

1983 ◽  
Vol 20 (04) ◽  
pp. 920-923 ◽  
Author(s):  
Hau Leung Lee ◽  
Morris A. Cohen
Keyword(s):  
Performance Measures ◽  
Waiting Time ◽  
Queueing System ◽  
Queueing Systems ◽  
Arrival Rate ◽  
Control Problems ◽  
Traffic Intensity ◽  
Expected Number ◽  
Expected Waiting Time

Convexity of performance measures of queueing systems is important in solving control problems of multi-facility systems. This note proves that performance measures such as the expected waiting time, expected number in queue, and the Erlang delay formula are convex with respect to the arrival rate or the traffic intensity of the M/M/c queueing system.

Waiting Time in M/G/1 Queues with Impolite Arrival Disciplines

1995 ◽  
Vol 9 (2) ◽  
pp. 255-267 ◽  
Author(s):  
Süleyman Òzekici ◽  
Jingwen Li ◽  
Fee Seng Chou
Keyword(s):  
Performance Measures ◽  
Waiting Time ◽  
Time Distribution ◽  
Iterative Procedure ◽  
Queueing System ◽  
Waiting Time Distribution ◽  
Special Model ◽  
Average Waiting Time ◽  
Random Position ◽  
Number Of Customers

We consider a queueing system where arriving customers join the queue at some random position. This constitutes an impolite arrival discipline because customers do not necessarily go to the end of the line upon arrival. Although mean performance measures like the average waiting time and average number of customers in the queue are the same for all such disciplines, we show that the variance of the waiting time increases as the arrival discipline becomes more impolite, in the sense that a customer is more likely to choose a position closer to the server. For the M/G/1 model, we also provide an iterative procedure for computing the moments of the waiting time distribution. Explicit computational formulas are derived for an interesting special model where a customer joins the queue either at the head or at the end of the line.

On berry–esseen rate for queue length of the GI/G/K system in heavy traffic

1988 ◽  
Vol 25 (03) ◽  
pp. 596-611
Author(s):  
Xing Jin
Keyword(s):  
Limit Theorem ◽  
Waiting Time ◽  
Queue Length ◽  
Queueing System ◽  
Heavy Traffic ◽  
Traffic Intensity ◽  
Main Method ◽  
Number Of Customers

This paper provides Berry–Esseen rate of limit theorem concerning the number of customers in a GI/G/K queueing system observed at arrival epochs for traffic intensity ρ > 1. The main method employed involves establishing several equalities about waiting time and queue length.

ANALYSIS OF A BULK QUEUE WITH FAST AND SLOW SERVICE RATES AND MULTIPLE VACATIONS

2005 ◽  
Vol 22 (02) ◽  
pp. 239-260 ◽  
Author(s):  
R. ARUMUGANATHAN ◽  
K. S. RAMASWAMI
Keyword(s):  
Performance Measures ◽  
Queue Length ◽  
Queueing System ◽  
Cost Model ◽  
Probability Generating Function ◽  
Service Rate ◽  
Multiple Vacations ◽  
Bulk Queue ◽  
Service Rates ◽  
Number Of Customers

We analyze a Mx/G(a,b)/1 queueing system with fast and slow service rates and multiple vacations. The server does the service with a faster rate or a slower rate based on the queue length. At a service completion epoch (or) at a vacation completion epoch if the number of customers waiting in the queue is greater than or equal to N (N > b), then the service is rendered at a faster rate, otherwise with a slower service rate. After finishing a service, if the queue length is less than 'a' the server leaves for a vacation of random length. When he returns from the vacation, if the queue length is still less than 'a' he leaves for another vacation and so on until he finally finds atleast 'a' customers waiting for service. After a service (or) a vacation, if the server finds atleast 'a' customers waiting for service say ξ, then he serves a batch of min (ξ, b) customers, where b ≥ a. We derive the probability generating function of the queue size at an arbitrary time. Various performance measures are obtained. A cost model is discussed with a numerical solution.

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