Priority queueing model with changeover times and switching threshold

2001 ◽  
Vol 38 (A) ◽  
pp. 263-273 ◽  
Author(s):  
Yonglu Deng ◽  
Jiqing Tan
Keyword(s):  
Generating Function ◽  
Probability Generating Function ◽  
Joint Probability ◽  
The Other ◽  
Analytic Method ◽  
Single Server ◽  
Switching Threshold ◽  
Mean Delay ◽  
Changeover Times ◽  
Priority Queueing

The paper studies a single-server two-queue priority system with changeover times and switching threshold. The server serves queue 1 exhaustively and does not remain at an empty queue if the other one is non-empty. It immediately switches from queue 2 to queue 1 when the length of the latter reaches some level M. Whenever service is changed from one queue to the other a changeover time is required. Arrivals are Poisson, service times and changeover times are independent and exponentially distributed. Using an analytic method we obtain the steady-state joint probability generating function of the lengths of the two queues. By means of this probability generating function some performance measures of the system such as mean length of queue and mean delay can be calculated.

Priority queueing model with changeover times and switching threshold

2001 ◽  
Vol 38 (A) ◽  
pp. 263-273 ◽  
Author(s):  
Yonglu Deng ◽  
Jiqing Tan
Keyword(s):  
Generating Function ◽  
Probability Generating Function ◽  
Joint Probability ◽  
The Other ◽  
Analytic Method ◽  
Single Server ◽  
Switching Threshold ◽  
Mean Delay ◽  
Changeover Times ◽  
Priority Queueing

The paper studies a single-server two-queue priority system with changeover times and switching threshold. The server serves queue 1 exhaustively and does not remain at an empty queue if the other one is non-empty. It immediately switches from queue 2 to queue 1 when the length of the latter reaches some level M. Whenever service is changed from one queue to the other a changeover time is required. Arrivals are Poisson, service times and changeover times are independent and exponentially distributed. Using an analytic method we obtain the steady-state joint probability generating function of the lengths of the two queues. By means of this probability generating function some performance measures of the system such as mean length of queue and mean delay can be calculated.

scholarly journals An M/G/l queueing system with fixed feedback policy

2002 ◽  
Vol 44 (2) ◽  
pp. 283-297 ◽  
Author(s):  
Bong Dae Choi ◽  
Bara Kim
Keyword(s):  
Response Time ◽  
Generating Function ◽  
Queueing System ◽  
Probability Generating Function ◽  
Joint Probability ◽  
Fixed Number ◽  
Single Server ◽  
Total Response ◽  
Stieltjes Transform ◽  
Total Response Time

We consider a single server queueing system where each customer visits the queue a fixed number of times before departure. A customer on his j th visit to the queue is defined to be a class-j -customer. We obtain the joint probability generating function for the number of class-j-customers and also obtain the Laplace-Stieltjes transform for the total response time of a customer.

scholarly journals A TWO-CLASS RETRIAL SYSTEM WITH COUPLED ORBIT QUEUES

2017 ◽  
Vol 31 (2) ◽  
pp. 139-179 ◽  
Author(s):  
Ioannis Dimitriou
Keyword(s):  
Performance Metrics ◽  
Kernel Method ◽  
Length Distribution ◽  
Probability Generating Function ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Single Server ◽  
Method Performance ◽  
Service Station ◽  
Queue Length Distribution

We consider a single server system accepting two types of retrial customers, which arrive according to two independent Poisson streams. The service station can handle at most one customer, and in case of blocking, typeicustomer,i=1, 2, is routed to a separate typeiorbit queue of infinite capacity. Customers from the orbits try to access the server according to the constant retrial policy. We consider coupled orbit queues, and thus, when both orbit queues are non-empty, the orbit queueitries to re-dispatch a blocked customer of typeito the main service station after an exponentially distributed time with rate μi. If an orbit queue empties, the other orbit queue changes its re-dispatch rate from μito$\mu_{i}^{\ast}$. We consider both exponential and arbitrary distributed service requirements, and show that the probability generating function of the joint stationary orbit queue length distribution can be determined using the theory of Riemann (–Hilbert) boundary value problems. For exponential service requirements, we also investigate the exact tail asymptotic behavior of the stationary joint probability distribution of the two orbits with either an idle or a busy server by using the kernel method. Performance metrics are obtained, computational issues are discussed and a simple numerical example is presented.

Traffic light queues as a generalization to queueing theory

1971 ◽  
Vol 8 (3) ◽  
pp. 480-493 ◽  
Author(s):  
Hisashi Mine ◽  
Katsuhisa Ohno
Keyword(s):  
Generating Function ◽  
Discrete Time ◽  
Queue Length ◽  
Length Distribution ◽  
Probability Generating Function ◽  
Traffic Light ◽  
Queue Length Distribution ◽  
Mean Delay ◽  
Stationary Queue Length ◽  
Stationary Queue Length Distribution

Fixed-cycle traffic light queues have been investigated by probabilistic methods by many authors. Beckmann, McGuire and Winsten (1956) considered a discrete time queueing model with binomial arrivals and regular departure headways and derived a relation between the stationary mean delay per vehicle and the stationary mean queue-length at the beginning of a red period of the traffic light. Haight (1959) and Buckley and Wheeler (1964) considered models with Poisson arrivals and regular departure headways and investigated certain properties of the queue-length. Newell (1960) dealt with the model proposed by the first authors and obtained the probability generating function of the stationary queue-length distribution. Darroch (1964) discussed a more general discrete time model with stationary, independent arrivals and regular departure headways and derived a necessary and sufficient condition for the stationary queue-length distribution to exist and obtained its probability generating function. The above two authors, Little (1961), Miller (1963), Newell (1965), McNeil (1968), Siskind (1970) and others gave approximate expressions for the stationary mean delay per vehicle for fixed-cycle traffic light queues of various types. All of the authors mentioned above dealt with the queue-length.

Queuing Scheme with Feedback Service and Discretionary Administration

2019 ◽  
Vol 9 (1S4) ◽  
pp. 706-710 ◽  
Keyword(s):  
Generating Function ◽  
Average Length ◽  
Probability Generating Function ◽  
Function Approach ◽  
Single Server ◽  
Queue Size ◽  
Supplementary Variable ◽  
Variable Technique ◽  
Supplementary Variable Technique ◽  
Central Organization

This article take a gander at a bunch area single server channel Queuing system, where the server gives two sorts of organizations viz., beginning one a central organization and the optional organization is permitted as a second organization. In case in need, the customer settle on the optional organization .We other than anticipate that after the execution of the second time of affiliation, if the structure is unfilled, the server takes a required get-away of general dissemination. Organization thwarts in the midst of principal organization at random. Additionally if the customer isn't satisfied with the primary central organization, an info advantage for the proportionate is given to make a worthy space for the customers in the system. For the above delineated covering issue, the supplementary variable technique and generating function approach are used to derive the probability generating function of the queue size and the average length of the queue.

Regenerative multivariate point processes

1978 ◽  
Vol 10 (2) ◽  
pp. 411-430 ◽  
Author(s):  
Mark Berman
Keyword(s):  
General Theory ◽  
Asymptotic Behaviour ◽  
Generating Function ◽  
Point Processes ◽  
Probability Generating Function ◽  
Joint Probability ◽  
Fixed Length ◽  
Multivariate Point ◽  
Monotonicity Results ◽  
Multivariate Point Processes

A class of stationary multivariate point processes is considered in which the events of one of the point processes act as regeneration points for the entire multivariate process. Some important properties of such processes are derived including the joint probability generating function for numbers of events in an interval of fixed length and the asymptotic behaviour of such processes. The general theory is then applied in three bivariate examples. Finally, some simple monotonicity results for stationary and renewal point processes (which are used in the second example) are proved in two appendices.

The generalised state-dependent queue: the busy period Erlangian

1974 ◽  
Vol 11 (03) ◽  
pp. 618-623
Author(s):  
B. W. Conolly
Keyword(s):  
Laplace Transform ◽  
Generating Function ◽  
Busy Period ◽  
Continued Fraction ◽  
Queueing System ◽  
Joint Probability ◽  
Single Server ◽  
System State ◽  
State Dependent ◽  
The Laplace Transform

A continued fraction representation is presented of the Laplace transform of the generating function of the fundamental joint probability and density of busy period length measured in customers served and duration in time. The setting is the single server Erlang queueing system where the parameters of negative exponentially distributed arrival and service times have a general dependence on instantaneous system state.

Regenerative multivariate point processes

1978 ◽  
Vol 10 (02) ◽  
pp. 411-430 ◽  
Author(s):  
Mark Berman
Keyword(s):  
General Theory ◽  
Asymptotic Behaviour ◽  
Generating Function ◽  
Point Processes ◽  
Probability Generating Function ◽  
Joint Probability ◽  
Fixed Length ◽  
Multivariate Point ◽  
Monotonicity Results ◽  
Multivariate Point Processes

A class of stationary multivariate point processes is considered in which the events of one of the point processes act as regeneration points for the entire multivariate process. Some important properties of such processes are derived including the joint probability generating function for numbers of events in an interval of fixed length and the asymptotic behaviour of such processes. The general theory is then applied in three bivariate examples. Finally, some simple monotonicity results for stationary and renewal point processes (which are used in the second example) are proved in two appendices.

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