scholarly journals On a generalization of the preemptive resume priority

1986 ◽  
Vol 18 (1) ◽  
pp. 255-273 ◽  
Author(s):  
Philippe Nain
Keyword(s):  
Communication Networks ◽  
Queueing System ◽  
Single Server ◽  
Stieltjes Transform ◽  
Priority Service ◽  
Service Interruption ◽  
Preemptive Resume ◽  
Class 1 ◽  
Potential Applications ◽  
Preemptive Resume Priority

This paper considers a queueing system with two classes of customers and a single server, where the service policy is of threshold type. As soon as the amount of work required by the class 1 customers is greater than a fixed threshold, the class 1 customers get the server's attention; otherwise the class 2 customers have the priority. Service interruptions can occur for both classes of customers on the basis of the above description of the service mechanism, and in this case the service interruption discipline is preemptive resume priority (PRP). This model, which turns out to be a generalization of the PRP queueing system, has potential applications in computer systems and in communication networks. For Poisson inputs, exponential (arbitrary) servicetime distribution for class 1 (class 2) customers, we derive the Laplace–Stieltjes transform of the stationary joint distribution of the workload of the server, by reducing the analysis to the resolution of a boundary value problem. Explicit formulas are obtained.

scholarly journals On a generalization of the preemptive resume priority

1986 ◽  
Vol 18 (01) ◽  
pp. 255-273
Author(s):  
Philippe Nain
Keyword(s):  
Communication Networks ◽  
Queueing System ◽  
Single Server ◽  
Stieltjes Transform ◽  
Priority Service ◽  
Service Interruption ◽  
Preemptive Resume ◽  
Class 1 ◽  
Potential Applications ◽  
Preemptive Resume Priority

This paper considers a queueing system with two classes of customers and a single server, where the service policy is of threshold type. As soon as the amount of work required by the class 1 customers is greater than a fixed threshold, the class 1 customers get the server's attention; otherwise the class 2 customers have the priority. Service interruptions can occur for both classes of customers on the basis of the above description of the service mechanism, and in this case the service interruption discipline is preemptive resume priority (PRP). This model, which turns out to be a generalization of the PRP queueing system, has potential applications in computer systems and in communication networks. For Poisson inputs, exponential (arbitrary) servicetime distribution for class 1 (class 2) customers, we derive the Laplace–Stieltjes transform of the stationary joint distribution of the workload of the server, by reducing the analysis to the resolution of a boundary value problem. Explicit formulas are obtained.

The single-server queue with service depending on queue size and with the preemptive-resume last-come–first-served queue discipline

1987 ◽  
Vol 24 (03) ◽  
pp. 758-767
Author(s):  
D. Fakinos
Keyword(s):  
Queueing System ◽  
Limiting Distribution ◽  
Single Server ◽  
Queue Size ◽  
Single Server Queue ◽  
Preemptive Resume ◽  
Server Queue ◽  
Queue Discipline ◽  
Service Times

This paper studies theGI/G/1 queueing system assuming that customers have service times depending on the queue size and also that they are served in accordance with the preemptive-resume last-come–first-served queue discipline. Expressions are given for the limiting distribution of the queue size and the remaining durations of the corresponding services, when the system is considered at arrival epochs, at departure epochs and continuously in time. Also these results are applied to some particular cases of the above queueing system.

On the stationary workload distribution of work-conserving single-server queues: a general formula via stochastic intensity

2001 ◽  
Vol 38 (3) ◽  
pp. 793-798 ◽  
Author(s):  
Naoto Miyoshi
Keyword(s):  
Closed Form ◽  
Queueing System ◽  
Marked Point ◽  
Marked Point Process ◽  
Single Server ◽  
Stochastic Intensity ◽  
Preemptive Resume ◽  
Workload Distribution ◽  
Stationary Workload ◽  
Closed Form Formula

It is well known that a simple closed-form formula exists for the stationary distribution of the workload in M/GI/1 queues. In this paper, we extend this to the general stationary framework. Namely, we consider a work-conserving single-server queueing system, where the sequence of customers’ arrival epochs and their service times is described as a general stationary marked point process, and we derive a closed-form formula for the stationary workload distribution. The key to our proof is two-fold: one is the Palm-martingale calculus, that is, the connection between the notion of Palm probability and that of stochastic intensity. The other is the preemptive-resume last-come, first-served discipline.

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.

The single-server queue with service depending on queue size and with the preemptive-resume last-come–first-served queue discipline

1987 ◽  
Vol 24 (3) ◽  
pp. 758-767 ◽  
Author(s):  
D. Fakinos
Keyword(s):  
Queueing System ◽  
Limiting Distribution ◽  
Single Server ◽  
Queue Size ◽  
Single Server Queue ◽  
Preemptive Resume ◽  
Server Queue ◽  
Queue Discipline ◽  
Service Times

This paper studies the GI/G/1 queueing system assuming that customers have service times depending on the queue size and also that they are served in accordance with the preemptive-resume last-come–first-served queue discipline. Expressions are given for the limiting distribution of the queue size and the remaining durations of the corresponding services, when the system is considered at arrival epochs, at departure epochs and continuously in time. Also these results are applied to some particular cases of the above queueing system.

On the single-server queue with the preemptive-resume last-come–first-served queue discipline

1986 ◽  
Vol 23 (01) ◽  
pp. 243-248
Author(s):  
D. Fakinos
Keyword(s):  
Equilibrium Distribution ◽  
Queueing System ◽  
Independent Random Variables ◽  
Single Server ◽  
Queue Size ◽  
Single Server Queue ◽  
Idle Period ◽  
Preemptive Resume ◽  
Server Queue ◽  
Queue Discipline

The paper considers the GI/G/1 queueing system under the assumption of a last-come–first-served queue discipline, where each customer begins service immediately upon his arrival. At the next arrival, the previous service is interrupted but no loss of service is involved. It has been shown that when the system is considered exclusively at arrival epochs or exclusively at departure epochs, then the equilibrium distribution of the queue-size is geometric, while the remaining durations of the corresponding services are independent random variables each one distributed as the idle period in the dual (inverse) queue. In this paper alternative simpler proofs of the above results are given.

On the stationary workload distribution of work-conserving single-server queues: a general formula via stochastic intensity

2001 ◽  
Vol 38 (03) ◽  
pp. 793-798
Author(s):  
Naoto Miyoshi
Keyword(s):  
Closed Form ◽  
Queueing System ◽  
Marked Point ◽  
Marked Point Process ◽  
Single Server ◽  
Stochastic Intensity ◽  
Preemptive Resume ◽  
Workload Distribution ◽  
Stationary Workload ◽  
Closed Form Formula

It is well known that a simple closed-form formula exists for the stationary distribution of the workload in M/GI/1 queues. In this paper, we extend this to the general stationary framework. Namely, we consider a work-conserving single-server queueing system, where the sequence of customers’ arrival epochs and their service times is described as a general stationary marked point process, and we derive a closed-form formula for the stationary workload distribution. The key to our proof is two-fold: one is the Palm-martingale calculus, that is, the connection between the notion of Palm probability and that of stochastic intensity. The other is the preemptive-resume last-come, first-served discipline.

scholarly journals M/M/1 Retrial queueing system with negative arrival under non-preemptive priority service

2014 ◽  
Vol 5 (2) ◽  
Author(s):  
A. Muthu Ganapathi Subramanian ◽  
G. Ayyappan ◽  
G. Sekar
Keyword(s):  
Queueing System ◽  
Numerical Study ◽  
Arrival Rate ◽  
Single Server ◽  
Preemptive Priority ◽  
Negative Customers ◽  
Retrial Queueing System ◽  
Priority Service ◽  
Retrial Queueing ◽  
Negative Arrivals

Consider a single server retrial queueing system with negative arrival under non-pre-emptive priority service in which three types of customers arrive in a poisson process with arrival rate λ1 for low priority customers and λ2 for high priority customers and λ3 for negative arrival. Low and high priority customers are identified as primary calls. The service times follow an exponential distribution with parameters μ1 and μ2 for low and high priority customers. The retrial and negative arrivals are introduced for low priority customers only. Gelenbe (1991) has introduced a new class of queueing processes in which customers are either positive or negative. Positive means a regular customer who is treated in the usual way by a server. Negative customers have the effect of deleting some customer in the queue. In the simplest version, a negative arrival removes an ordinary positive customer or a random batch of positive customers according to some strategy. It is noted that the existence of a flow of negative arrivals provides a control mechanismto control excessive congestion at the retrial group and also assume that the negative customers only act when the server is busy. Let K be the maximumnumber of waiting spaces for high priority customers in front of the service station. The high priorities customers will be governed by the Non-preemptive priority service. The access from the orbit to the service facility is governed by the classical retrial policy. This model is solved by using Matrix geometric Technique. Numerical study have been done for Analysis of Mean number of low priority customers in the orbit (MNCO), Mean number of high priority customers in the queue(MPQL),Truncation level (OCUT),Probability of server free and Probabilities of server busy with low and high priority customers for various values of λ1 , λ2 , λ3 , μ1 , μ2 ,σ and k in elaborate manner and also various particular cases of this model have been discussed.

On the single-server queue with the preemptive-resume last-come–first-served queue discipline

1986 ◽  
Vol 23 (1) ◽  
pp. 243-248 ◽  
Author(s):  
D. Fakinos
Keyword(s):  
Equilibrium Distribution ◽  
Queueing System ◽  
Independent Random Variables ◽  
Single Server ◽  
Queue Size ◽  
Single Server Queue ◽  
Idle Period ◽  
Preemptive Resume ◽  
Server Queue ◽  
Queue Discipline

The paper considers the GI/G/1 queueing system under the assumption of a last-come–first-served queue discipline, where each customer begins service immediately upon his arrival. At the next arrival, the previous service is interrupted but no loss of service is involved. It has been shown that when the system is considered exclusively at arrival epochs or exclusively at departure epochs, then the equilibrium distribution of the queue-size is geometric, while the remaining durations of the corresponding services are independent random variables each one distributed as the idle period in the dual (inverse) queue. In this paper alternative simpler proofs of the above results are given.

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