scholarly journals The delay distribution of a type k customer in a first-come-first-served MMAP[K]/PH[K]/1 queue

2002 ◽  
Vol 39 (1) ◽  
pp. 213-223 ◽  
Author(s):  
B. Van Houdt ◽  
C. Blondia
Keyword(s):  
Discrete Time ◽  
Analytical Methods ◽  
Queueing System ◽  
Batch Arrivals ◽  
Numerical Examples ◽  
Delay Distribution ◽  
Type K ◽  
Arrival Processes ◽  
Algorithmic Procedure

This paper presents an algorithmic procedure to calculate the delay distribution of a type k customer in a first-come-first-served (FCFS) discrete-time queueing system with multiple types of customers, where each type has different service requirements (the MMAP[K]/PH[K]/1 queue). First, we develop a procedure, using matrix analytical methods, to handle arrival processes that do not allow batch arrivals to occur. Next, we show that this technique can be generalized to arrival processes that do allow batch arrivals to occur. We end the paper by presenting some numerical examples.

scholarly journals The delay distribution of a type k customer in a first-come-first-served MMAP[K]/PH[K]/1 queue

2002 ◽  
Vol 39 (01) ◽  
pp. 213-223
Author(s):  
B. Van Houdt ◽  
C. Blondia
Keyword(s):  
Discrete Time ◽  
Analytical Methods ◽  
Queueing System ◽  
Batch Arrivals ◽  
Numerical Examples ◽  
Delay Distribution ◽  
Type K ◽  
Arrival Processes ◽  
Algorithmic Procedure

This paper presents an algorithmic procedure to calculate the delay distribution of a type k customer in a first-come-first-served (FCFS) discrete-time queueing system with multiple types of customers, where each type has different service requirements (the MMAP[K]/PH[K]/1 queue). First, we develop a procedure, using matrix analytical methods, to handle arrival processes that do not allow batch arrivals to occur. Next, we show that this technique can be generalized to arrival processes that do allow batch arrivals to occur. We end the paper by presenting some numerical examples.

scholarly journals A discrete-time queueing system with changes in the vacation times

2016 ◽  
Vol 26 (2) ◽  
pp. 379-390 ◽  
Author(s):  
Ivan Atencia
Keyword(s):  
Performance Measures ◽  
Discrete Time ◽  
Busy Period ◽  
Queueing System ◽  
Probability Generating Function ◽  
Service Discipline ◽  
Numerical Examples ◽  
Extensive Analysis ◽  
The One ◽  
Steady State Performance

Abstract This paper considers a discrete-time queueing system in which an arriving customer can decide to follow a last come first served (LCFS) service discipline or to become a negative customer that eliminates the one at service, if any. After service completion, the server can opt for a vacation time or it can remain on duty. Changes in the vacation times as well as their associated distribution are thoroughly studied. An extensive analysis of the system is carried out and, using a probability generating function approach, steady-state performance measures such as the first moments of the busy period of the queue content and of customers delay are obtained. Finally, some numerical examples to show the influence of the parameters on several performance characteristics are given.

scholarly journals Controllability and Observability of Linear Discrete-Time Fractional-Order Systems

2008 ◽  
Vol 18 (2) ◽  
pp. 213-222 ◽  
Author(s):  
Said Guermah ◽  
Said Djennoune ◽  
Maamar Bettayeb
Keyword(s):  
Structural Properties ◽  
Fractional Order ◽  
Discrete Time ◽  
Analytical Methods ◽  
Fractional Order Systems ◽  
Numerical Examples ◽  
New Concepts ◽  
Controllability And Observability ◽  
Theoretical Results

Controllability and Observability of Linear Discrete-Time Fractional-Order SystemsIn this paper we extend some basic results on the controllability and observability of linear discrete-time fractional-order systems. For both of these fundamental structural properties we establish some new concepts inherent to fractional-order systems and we develop new analytical methods for checking these properties. Numerical examples are presented to illustrate the theoretical results.

A Discrete-Time Queueing Model with Service Upgrade

2014 ◽  
Vol 513-517 ◽  
pp. 806-811
Author(s):  
Ivan Atencia ◽  
Inmaculada Fortes ◽  
Sixto Sánchez
Keyword(s):  
Discrete Time ◽  
Generating Functions ◽  
Busy Period ◽  
Queueing System ◽  
Queueing Model ◽  
Numerical Examples ◽  
Extensive Analysis ◽  
Number Of Customers ◽  
Incoming Message

In this paper we analyze a discrete-time queueing system where the server decides whento upgrade the service depending on the information carried by the incoming message. We carry outan extensive analysis of the system developing recursive formulae and generating functions for thestationary distribution of the number of customers in the queue, the system, the busy period and thesojourntimeas well as some numerical examples.

scholarly journals A Novel Analytic Technique for the Service Station Reliability in a Discrete-Time Repairable Queue

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Renbin Liu ◽  
Yinghui Tang
Keyword(s):  
Reliability Analysis ◽  
Discrete Time ◽  
Queueing System ◽  
Queueing Systems ◽  
Decomposition Technique ◽  
Service Station ◽  
Numerical Examples ◽  
Reliability Indices ◽  
Special Cases ◽  
Bulk Arrival

This paper presents a decomposition technique for the service station reliability in a discrete-time repairableGeomX/G/1 queueing system, in which the server takes exhaustive service and multiple adaptive delayed vacation discipline. Using such a novel analytic technique, some important reliability indices and reliability relation equations of the service station are derived. Furthermore, the structures of the service station indices are also found. Finally, special cases and numerical examples validate the derived results and show that our analytic technique is applicable to reliability analysis of some complex discrete-time repairable bulk arrival queueing systems.

scholarly journals A Discrete-Time Queue with Preferred Customers and Partial Buffer Sharing

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Shizhong Zhou ◽  
Liwei Liu ◽  
Jianjun Li
Keyword(s):  
Discrete Time ◽  
Queueing System ◽  
Probability Generating Function ◽  
Necessary And Sufficient Condition ◽  
Arrival Processes ◽  
Novel Method ◽  
Buffer Sharing ◽  
Necessary And Sufficient ◽  
Waiting Line ◽  
Number Of Customers

We analyze a discrete-time Geo/Geo/1 queueing system with preferred customers and partial buffer sharing. In this model, customers arrive according to geometrical arrival processes with probabilityλ. If an arriving customer finds the server idle, he begins instantly his services. Otherwise, if the server is busy at the arrival epoch, the arrival either interrupts the customer being served to commence his own service with probabilityθ(the customer is called the preferred customer) or joins the waiting line at the back of the queue with probabilityθ~(the customer is called the normal customer) if permitted. The interrupted customer joins the waiting line at the head of the queue. If the total number of customers in the system is equal to or more than thresholdN, the normal customer will be ignored to enter into the system. But this restriction is not suitable for the preferred customers; that is, this system never loses preferred customers. A necessary and sufficient condition for the system to be stable is investigated and the stationary distribution of the queue length of the system is also obtained. Further, we develop a novel method to solve the probability generating function of the busy period of the system. The distribution of sojourn time of a customer in the server and the other indexes are acquired as well.

scholarly journals From Exhaustive Vacation Queues to Preemptive Priority Queues with General Interarrival Times

2018 ◽  
Vol 28 (4) ◽  
pp. 695-704
Author(s):  
Dieter Fiems ◽  
Stijn De Vuyst
Keyword(s):  
Discrete Time ◽  
Queueing System ◽  
Queueing Systems ◽  
Probability Generating Function ◽  
Priority Queue ◽  
Preemptive Priority ◽  
Numerical Examples ◽  
Preemptive Resume ◽  
Completion Times ◽  
Priority Queueing

Abstract We consider the discrete-time G/GI/1 queueing system with multiple exhaustive vacations. By a transform approach, we obtain an expression for the probability generating function of the waiting time of customers in such a system. We then show that the results can be used to assess the performance of G/GI/1 queueing systems with server breakdowns as well as that of the low-priority queue of a preemptive MX+G/GI/1 priority queueing system. By calculating service completion times of low-priority customers, various preemptive breakdown/priority disciplines can be studied, including preemptive resume and preemptive repeat, as well as their combinations. We illustrate our approach with some numerical examples.

Sign in / Sign up

Export Citation Format

Share Document