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 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.

scholarly journals Markovian Queueing System with Discouraged Arrivals and Self-Regulatory Servers

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
K. V. Abdul Rasheed ◽  
M. Manoharan
Keyword(s):  
Queueing System ◽  
Queueing Systems ◽  
Single Server ◽  
Expected Number ◽  
Multiple Servers ◽  
Special Cases ◽  
Service Rates ◽  
Expected Waiting Time ◽  
Number Of Customers ◽  
Steady State Probabilities

We consider discouraged arrival of Markovian queueing systems whose service speed is regulated according to the number of customers in the system. We will reduce the congestion in two ways. First we attempt to reduce the congestion by discouraging the arrivals of customers from joining the queue. Secondly we reduce the congestion by introducing the concept of service switches. First we consider a model in which multiple servers have three service ratesμ1,μ2, andμ(μ1≤μ2<μ), say, slow, medium, and fast rates, respectively. If the number of customers in the system exceeds a particular pointK1orK2, the server switches to the medium or fast rate, respectively. For this adaptive queueing system the steady state probabilities are derived and some performance measures such as expected number in the system/queue and expected waiting time in the system/queue are obtained. Multiple server discouraged arrival model having one service switch and single server discouraged arrival model having one and two service switches are obtained as special cases. A Matlab program of the model is presented and numerical illustrations are given.

scholarly journals A new look at transient versions of Little's law, and M/G/1 preemptive last-come-first-served queues

2010 ◽  
Vol 47 (2) ◽  
pp. 459-473 ◽  
Author(s):  
Brian H. Fralix ◽  
Germán Riaño
Keyword(s):  
Point Processes ◽  
Queueing System ◽  
Queueing Systems ◽  
Time Dependent ◽  
Structural Form ◽  
Preemptive Resume ◽  
Special Cases ◽  
Number Of Customers ◽  
Regulated Brownian Motion ◽  
New Look

We take a new look at transient, or time-dependent Little laws for queueing systems. Through the use of Palm measures, we show that previous laws (see Bertsimas and Mourtzinou (1997)) can be generalized. Furthermore, within this framework, a new law can be derived as well, which gives higher-moment expressions for very general types of queueing system; in particular, the laws hold for systems that allow customers to overtake one another. What is especially novel about our approach is the use of Palm measures that are induced by nonstationary point processes, as these measures are not commonly found in the queueing literature. This new higher-moment law is then used to provide expressions for all moments of the number of customers in the system in an M/G/1 preemptive last-come-first-served queue at a time t > 0, for any initial condition and any of the more famous preemptive disciplines (i.e. preemptive-resume, and preemptive-repeat with and without resampling) that are analogous to the special cases found in Abate and Whitt (1987c), (1988). These expressions are then used to derive a nice structural form for all of the time-dependent moments of a regulated Brownian motion (see Abate and Whitt (1987a), (1987b)).

scholarly journals A bulk queueing system under N-policy with bilevel service delay discipline and start-up time

1993 ◽  
Vol 6 (4) ◽  
pp. 359-384 ◽  
Author(s):  
David C. R. Muh
Keyword(s):  
Queue Length ◽  
Queueing System ◽  
Probability Generating Function ◽  
Single Server ◽  
Numerical Examples ◽  
Queueing Process ◽  
Poisson Input ◽  
Service Delay ◽  
Start Up ◽  
Bulk Arrival

The author studies the queueing process in a single-server, bulk arrival and batch service queueing system with a compound Poisson input, bilevel service delay discipline, start-up time, and a fixed accumulation level with control operating policy. It is assumed that when the queue length falls below a predefined level r(≥1), the system, with server capacity R, immediately stops service until the queue length reaches or exceeds the second predefined accumulation level N(≥r). Two cases, with N≤R and N≥R, are studied.The author finds explicitly the probability generating function of the stationary distribution of the queueing process and gives numerical examples.

scholarly journals Discrete-Time Bulk Queueing System with Variable Service Capacity Depending on Previous Service Time

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Yutae Lee
Keyword(s):  
Generating Function ◽  
Discrete Time ◽  
Service Time ◽  
Queue Length ◽  
Queueing System ◽  
Function Technique ◽  
Supplementary Variable ◽  
Service Capacity ◽  
Bulk Service ◽  
Bulk Arrival

This paper considers a discrete-time bulk-arrival bulk-service queueing system with variable service capacity, where the service capacity varies depending on the previous service time. Using the supplementary variable method and the generating function technique, we obtain the queue length distributions at arbitrary slot boundaries and service completion epochs.

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 A new look at transient versions of Little's law, and M/G/1 preemptive last-come-first-served queues

2010 ◽  
Vol 47 (02) ◽  
pp. 459-473 ◽  
Author(s):  
Brian H. Fralix ◽  
Germán Riaño
Keyword(s):  
Point Processes ◽  
Queueing System ◽  
Queueing Systems ◽  
Time Dependent ◽  
Structural Form ◽  
Preemptive Resume ◽  
Special Cases ◽  
Number Of Customers ◽  
Regulated Brownian Motion ◽  
New Look

We take a new look at transient, or time-dependent Little laws for queueing systems. Through the use of Palm measures, we show that previous laws (see Bertsimas and Mourtzinou (1997)) can be generalized. Furthermore, within this framework, a new law can be derived as well, which gives higher-moment expressions for very general types of queueing system; in particular, the laws hold for systems that allow customers to overtake one another. What is especially novel about our approach is the use of Palm measures that are induced by nonstationary point processes, as these measures are not commonly found in the queueing literature. This new higher-moment law is then used to provide expressions for all moments of the number of customers in the system in an M/G/1 preemptive last-come-first-served queue at a time t &gt; 0, for any initial condition and any of the more famous preemptive disciplines (i.e. preemptive-resume, and preemptive-repeat with and without resampling) that are analogous to the special cases found in Abate and Whitt (1987c), (1988). These expressions are then used to derive a nice structural form for all of the time-dependent moments of a regulated Brownian motion (see Abate and Whitt (1987a), (1987b)).

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.

Sign in / Sign up

Export Citation Format

Share Document