Multi-server queueing system with a generalized phase-type service time distribution as a model of call center with a call-back option

2014 ◽  
Vol 239 (2) ◽  
pp. 401-428 ◽  
Author(s):  
Alexander Dudin ◽  
Chesoong Kim ◽  
Olga Dudina ◽  
Sergey Dudin
Keyword(s):  
Service Time ◽  
Call Center ◽  
Time Distribution ◽  
Queueing System ◽  
Service Time Distribution ◽  
Phase Type ◽  
Multi Server

A BMAP/PH/N SYSTEM WITH IMPATIENT REPEATED CALLS

2007 ◽  
Vol 24 (03) ◽  
pp. 293-312 ◽  
Author(s):  
VALENTINA I. KLIMENOK ◽  
DMITRY S. ORLOVSKY ◽  
ALEXANDER N. DUDIN
Keyword(s):  
Markov Chain ◽  
Time Distribution ◽  
Arrival Process ◽  
Service Time Distribution ◽  
State Distribution ◽  
Unsuccessful Attempt ◽  
Batch Markovian Arrival Process ◽  
Repeated Calls ◽  
Phase Type ◽  
Multi Server

A multi-server queueing model with a Batch Markovian Arrival Process, phase-type service time distribution and impatient repeated customers is analyzed. After any unsuccessful attempt, the repeated customer leaves the system with the fixed probability. The behavior of the system is described in terms of continuous time multi-dimensional Markov chain. Stability condition and an algorithm for calculating the stationary state distribution of this Markov chain are obtained. Main performance measures of the system are calculated. Numerical results are presented.

Some results on regular variation for distributions in queueing and fluctuation theory

1973 ◽  
Vol 10 (2) ◽  
pp. 343-353 ◽  
Author(s):  
J. W. Cohen
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Regular Variation ◽  
Time Distribution ◽  
Queueing System ◽  
Sufficient Conditions ◽  
Distribution Functions ◽  
Service Time Distribution ◽  
Virtual Waiting Time ◽  
Necessary And Sufficient

For the distribution functions of the stationary actual waiting time and of the stationary virtual waiting time of the GI/G/l queueing system it is shown that the tails vary regularly at infinity if and only if the tail of the service time distribution varies regularly at infinity.For sn the sum of n i.i.d. variables xi, i = 1, …, n it is shown that if E {x1} < 0 then the distribution of sup, s1s2, …] has a regularly varying tail at + ∞ if the tail of the distribution of x1 varies regularly at infinity and conversely, moreover varies regularly at + ∞.In the appendix a lemma and its proof are given providing necessary and sufficient conditions for regular variation of the tail of a compound Poisson distribution.

ANALYSIS OF A MULTI-SERVER QUEUE WITH MARKOVIAN ARRIVALS AND SYNCHRONOUS PHASE TYPE VACATIONS

2009 ◽  
Vol 26 (01) ◽  
pp. 85-113 ◽  
Author(s):  
SRINIVAS R. CHAKRAVARTHY
Keyword(s):  
Steady State ◽  
Time Distribution ◽  
Queueing System ◽  
Queueing Model ◽  
Waiting Time Distribution ◽  
Steady State Analysis ◽  
Phase Type ◽  
Server Queue ◽  
Qbd Process ◽  
Multi Server

We study a MAP/M/c queueing system in which a group of servers take a simultaneous phase type vacation. The queueing model is studied as a QBD process. The steady-state analysis of the model including the waiting time distribution is presented. Interesting numerical results are discussed.

Rate conservation for stationary processes

1991 ◽  
Vol 28 (1) ◽  
pp. 146-158 ◽  
Author(s):  
Josep M. Ferrandiz ◽  
Aurel A. Lazar
Keyword(s):  
Service Time ◽  
Conservation Law ◽  
Time Distribution ◽  
Distribution Density ◽  
Queueing System ◽  
Arrival Process ◽  
Stationary Processes ◽  
Service Time Distribution ◽  
Stochastic Intensity ◽  
Residual Service

We derive a rate conservation law for distribution densities which extends a result of Brill and Posner. Based on this conservation law, we obtain a generalized Takács equation for the G/G/m/B queueing system that only requires the existence of a stochastic intensity for the arrival process and the residual service time distribution density for the G/GI/1/B queue. Finally, we solve Takács' equation for the N/GI/1/∞ queueing system.

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