Transient solution to the many-server Poisson queue: a simple approach

1989 ◽  
Vol 26 (3) ◽  
pp. 584-594 ◽  
Author(s):  
P. R. Parthasarathy ◽  
M. Sharafali
Keyword(s):  
Queueing System ◽  
Simple Approach ◽  
Time Dependent ◽  
Transient Solution ◽  
The Many ◽  
Time Dependent Solution

An elegant time-dependent solution for the number in the M/M/c queueing system is derived in a direct way.

Transient solution to the many-server Poisson queue: a simple approach

1989 ◽  
Vol 26 (03) ◽  
pp. 584-594 ◽  
Author(s):  
P. R. Parthasarathy ◽  
M. Sharafali
Keyword(s):  
Queueing System ◽  
Simple Approach ◽  
Time Dependent ◽  
Transient Solution ◽  
The Many ◽  
Time Dependent Solution

An elegant time-dependent solution for the number in the M/M/c queueing system is derived in a direct way.

scholarly journals A transient solution to an M/M/1 queue: a simple approach

1987 ◽  
Vol 19 (04) ◽  
pp. 997-998 ◽  
Author(s):  
P. R. Parthasarathy
Keyword(s):  
Queueing System ◽  
Simple Approach ◽  
Time Dependent ◽  
Single Server ◽  
Transient Solution ◽  
Poisson Arrivals ◽  
Service Times ◽  
Time Dependent Solution

A time-dependent solution for the number in a single-server queueing system with Poisson arrivals and exponential service times is derived in a direct way.

scholarly journals A transient solution to an M/M/1 queue: a simple approach

1987 ◽  
Vol 19 (4) ◽  
pp. 997-998 ◽  
Author(s):  
P. R. Parthasarathy
Keyword(s):  
Queueing System ◽  
Simple Approach ◽  
Time Dependent ◽  
Single Server ◽  
Transient Solution ◽  
Poisson Arrivals ◽  
Service Times ◽  
Time Dependent Solution

A time-dependent solution for the number in a single-server queueing system with Poisson arrivals and exponential service times is derived in a direct way.

Time-dependent solution and optimal control of a bulk service queue

1997 ◽  
Vol 34 (01) ◽  
pp. 258-266
Author(s):  
Shokri Z. Selim
Keyword(s):  
Queueing System ◽  
Maximum Size ◽  
Time Dependent ◽  
Optimal Service ◽  
Bulk Service ◽  
Service Rates ◽  
Finite Time Horizon ◽  
Number Of Customers ◽  
Time Dependent Solution ◽  
Dependent Probability

We consider the queueing system denoted by M/MN /1/N where customers are served in batches of maximum size N. The model is motivated by a traffic application. The time-dependent probability distribution for the number of customers in the system is obtained in closed form. The solution is used to predict the optimal service rates during a finite time horizon.

Time-dependent solution and optimal control of a bulk service queue

1997 ◽  
Vol 34 (1) ◽  
pp. 258-266 ◽  
Author(s):  
Shokri Z. Selim
Keyword(s):  
Queueing System ◽  
Maximum Size ◽  
Time Dependent ◽  
Optimal Service ◽  
Bulk Service ◽  
Service Rates ◽  
Finite Time Horizon ◽  
Number Of Customers ◽  
Time Dependent Solution ◽  
Dependent Probability

We consider the queueing system denoted by M/MN/1/N where customers are served in batches of maximum size N. The model is motivated by a traffic application. The time-dependent probability distribution for the number of customers in the system is obtained in closed form. The solution is used to predict the optimal service rates during a finite time horizon.

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.

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