Abstract
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Award date  1 Jan 2007 
Place of Publication  Chapel Hill 
Publisher  
Publication status  Published  2007 
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Service systems with balking based on queueing time. / Liu, L.Q.
Chapel Hill : University of North Carolina, 2007. 95 p.Research output: Thesis › Phd Thesis 4 Research NOT TU/e / Graduation NOT TU/e)
TY  THES
T1  Service systems with balking based on queueing time
AU  Liu, L.Q.
PY  2007
Y1  2007
N2  We consider service systems with balking based on queueing time, also called queues with waitbased balking. An arriving customer joins the queue and stays until served if and only if the queueing time is no more than some prespecified threshold at the time of arrival. We assume that the arrival process is a Poisson process. We begin with the study of theM/G/1 system with a deterministic balking threshold. We use levelcrossing argument to derive an integral equation for the steady state virtual queueing time (vqt) distribution. We describe a procedure to solve the equation for general distributions and we solve the equation explicitly for several special cases of service time distributions, such as phase type, Erlang, exponential and deterministic service times. We give formulas for several performance criteria of general interest, including average queueing time and balking rate. We illustrate the results with numerical examples. We then consider the first passage time problem in an M/PH/1 setting. We use a fluid model where the buffer content changes at a rate determined by an external stochastic process with finite state space. We derive systems of firstorder linear differential equations for both the mean and LST (LaplaceStieltjes Transform) of the busy period in the fluid model and solve them explicitly. We obtain the mean and LST of the busy period in the M/PH/1 queue with waitbased balking as a special limiting case of the fluid model. We illustrate the results with numerical examples. Finally we extend the method used in the single server case to multiserver case. We consider the vqt process in an M/G/s queue with waitbased balking. We construct a single server system, analyze its operating characteristics, and use it to approximate the multiserver system. The approximation is exact for the M/M/s and M/G/1 system. We give both analytical results and numerical examples. We conduct simulation to assess the accuracy of the approximation.
AB  We consider service systems with balking based on queueing time, also called queues with waitbased balking. An arriving customer joins the queue and stays until served if and only if the queueing time is no more than some prespecified threshold at the time of arrival. We assume that the arrival process is a Poisson process. We begin with the study of theM/G/1 system with a deterministic balking threshold. We use levelcrossing argument to derive an integral equation for the steady state virtual queueing time (vqt) distribution. We describe a procedure to solve the equation for general distributions and we solve the equation explicitly for several special cases of service time distributions, such as phase type, Erlang, exponential and deterministic service times. We give formulas for several performance criteria of general interest, including average queueing time and balking rate. We illustrate the results with numerical examples. We then consider the first passage time problem in an M/PH/1 setting. We use a fluid model where the buffer content changes at a rate determined by an external stochastic process with finite state space. We derive systems of firstorder linear differential equations for both the mean and LST (LaplaceStieltjes Transform) of the busy period in the fluid model and solve them explicitly. We obtain the mean and LST of the busy period in the M/PH/1 queue with waitbased balking as a special limiting case of the fluid model. We illustrate the results with numerical examples. Finally we extend the method used in the single server case to multiserver case. We consider the vqt process in an M/G/s queue with waitbased balking. We construct a single server system, analyze its operating characteristics, and use it to approximate the multiserver system. The approximation is exact for the M/M/s and M/G/1 system. We give both analytical results and numerical examples. We conduct simulation to assess the accuracy of the approximation.
UR  http://stator.unc.edu/webspace/webpage/Tech_rep/Liqiang_diss.pdf
M3  Phd Thesis 4 Research NOT TU/e / Graduation NOT TU/e)
PB  University of North Carolina
CY  Chapel Hill
ER 