Analysis of a Two-Phase Queueing System with a Markov Arrival Process and Losses

2005 ◽  
Vol 131 (3) ◽  
pp. 5606-5613 ◽  
Author(s):  
P. P. Bocharov ◽  
R. Manzo ◽  
A. V. Pechinkin
Keyword(s):  
Queueing System ◽  
Arrival Process ◽  
Two Phase ◽  
Markov Arrival ◽  
Markov Arrival Process

Two-Phase Queueing System with a Markov Arrival Process and Blocking

2006 ◽  
Vol 132 (5) ◽  
pp. 578-589 ◽  
Author(s):  
P. P. Bocharov ◽  
R. Manzo ◽  
A. V. Pechinkin
Keyword(s):  
Queueing System ◽  
Arrival Process ◽  
Two Phase ◽  
Markov Arrival ◽  
Markov Arrival Process

scholarly journals Analysis of Multi-Server Queue with Self-Sustained Servers

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2134
Author(s):  
Alexander Dudin ◽  
Olga Dudina ◽  
Sergei Dudin ◽  
Konstantin Samouylov
Keyword(s):  
Three Dimensional ◽  
Optimal Choice ◽  
Arrival Process ◽  
Queuing Model ◽  
Numerical Result ◽  
Self Sufficiency ◽  
Server Queue ◽  
Markov Arrival ◽  
Markov Arrival Process ◽  
Multi Server

A novel multi-server vacation queuing model is considered. The distinguishing feature of the model, compared to the standard queues, is the self-sufficiency of servers. A server can terminate service and go on vacation independently of the system manager and the overall situation in the system. The system manager can make decisions whether to allow the server to start work after vacation completion and when to try returning some server from a vacation to process customers. The arrival flow is defined by a general batch Markov arrival process. The problem of optimal choice of the total number of servers and the thresholds defining decisions of the manager arises. To solve this problem, the behavior of the system is described by the three-dimensional Markov chain with the special block structure of the generator. Conditions for the ergodicity of this chain are derived, the problem of computation of the steady-state distribution of the chain is discussed. Expressions for the key performance indicators of the system in terms of the distribution of the chain states are derived. An illustrative numerical result is presented.

Two-Phase Resource Queueing System with Requests Duplication and Renewal Arrival Process

2020 ◽  
pp. 350-364
Author(s):  
Anastasia Galileyskaya ◽  
Ekaterina Lisovskaya ◽  
Michele Pagano ◽  
Svetlana Moiseeva
Keyword(s):  
Queueing System ◽  
Arrival Process ◽  
Two Phase

COMPARISON OF QUEUES WITH DIFFERENT DISCRETE-TIME ARRIVAL PROCESSES

2001 ◽  
Vol 15 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Arie Hordijk
Keyword(s):  
Lower Bound ◽  
Discrete Time ◽  
Sojourn Time ◽  
Arrival Process ◽  
Convex Ordering ◽  
Arrival Processes ◽  
Markov Arrival ◽  
Markov Arrival Process ◽  
Special Case ◽  
Stochastic Event

Traveling times in a FIFO-stochastic event graph are compared in increasing convex ordering for different arrival processes. As a special case, a stochastic lower bound is obtained for the sojourn time in a tandem network of FIFO queues with a Markov arrival process. A counterexample shows that the extended Ross conjecture is not true for discrete-time arrival processes.

Performance Approximation for Time-Dependent Queues with Generally Distributed Abandonments

2021 ◽  
Author(s):  
Gregor Selinka ◽  
Raik Stolletz ◽  
Thomas I. Maindl
Keyword(s):  
Performance Measures ◽  
Real World ◽  
Queueing System ◽  
Time Dependent ◽  
Interval Length ◽  
Arrival Process ◽  
Real World Data ◽  
World Data ◽  
Extant Literature ◽  
Approximation Quality

Many stochastic systems face a time-dependent demand. Especially in stochastic service systems, for example, in call centers, customers may leave the queue if their waiting time exceeds their personal patience. As discussed in the extant literature, it can be useful to use general distributions to model such customer patience. This paper analyzes the time-dependent performance of a multiserver queue with a nonhomogeneous Poisson arrival process with a time-dependent arrival rate, exponentially distributed processing times, and generally distributed time to abandon. Fast and accurate performance approximations are essential for decision support in such queueing systems, but the extant literature lacks appropriate methods for the setting we consider. To approximate time-dependent performance measures for small- and medium-sized systems, we develop a new stationary backlog-carryover (SBC) approach that allows for the analysis of underloaded and overloaded systems. Abandonments are considered in two steps of the algorithm: (i) in the approximation of the utilization as a reduced arrival stream and (ii) in the approximation of waiting-based performance measures with a stationary model for general abandonments. To improve the approximation quality, we discuss an adjustment to the interval lengths. We present a limit result that indicates convergence of the method for stationary parameters. The numerical study compares the approximation quality of different adjustments to the interval length. The new SBC approach is effective for instances with small numbers of time-dependent servers and gamma-distributed abandonment times with different coefficients of variation and for an empirical distribution of the abandonment times from real-world data obtained from a call center. A discrete-event simulation benchmark confirms that the SBC algorithm approximates the performance of the queueing system with abandonments very well for different parameter configurations. Summary of Contribution: The paper presents a fast and accurate numerical method to approximate the performance measures of a time‐dependent queueing system with generally distributed abandonments. The presented stationary backlog carryover approach with abandonment combines algorithmic ideas with stationary queueing models for generally distributed abandonment times. The reliability of the method is analyzed for transient systems and numerically studied with real‐world data.

A queueing system with non-recurrent input and batch servicing

1965 ◽  
Vol 2 (02) ◽  
pp. 442-448
Author(s):  
C. Pearce
Keyword(s):  
Distribution Function ◽  
Queueing System ◽  
Arrival Process ◽  
Batch Service ◽  
Service Times

We consider a queueing system in which arrivals occur at times , and after every kth arrival a servicing of k arrivals is begun. We assume that the number of servers is infinite. Initially, at t 0 = 0, the system is empty and the arrival process {tn } is about to start. The batch service times are independently and identically distributed with distribution function No assumption is made about the process {tn }.

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