Transient analysis of a two-heterogeneous servers queue with impatient behavior

AbstractRecently, [1] have obtained the transient solution of multi-server queue with balking and reneging. In this paper, a similar technique is used to drive a new elegant explicit solution for a two heterogeneous servers queue with impatient behavior. In addition, steady-state probabilities of the system size are studied and some important performance measures are discussed for the considered system

Analytical Study of Two Serial Channels with Priority and Reneging

Most of the studies of queuing theory, which are useful in our daily life has been investigated by many researchers. The present research is the study of pre-emptive priority queuing system consisting two serial channels in stochastic environment. The impatient behavior of customer’s will be discussed with exponential service distribution and Poisson arrivals. Higher priority customers have pre-emptive priority over the low priority customers. The G.F. technique is used to derive the performance measures of high & low priority queues and assuming FCFS discipline in busy schedule of higher priority class. Also evaluate queue behavior graphically and discussed a special case at the end which shows utilization of channels

Ticket Queues - Modeling, Analysis and Strategic Customer Behavior

Ανάλυση και μέθοδοι μοντελοποίησης σε ουρές αναμονής όπου κατά την άφιξη πελάτη στο σύστημα εκδίδεται εισητήριο με εκτυπωμένο αριθμό προτεραιότητας. Παρουσιάζονται δύο μοντέλα με διαφορετικούς τύπους αποθαρρυνόμενων πελατών και στρατηγικές κατωφλιού.Analysis and modeling methods for queues where upon a customer's arrival in the system, s/he is issued with a ticket which has a priority number printed on it. There are presented two different models (with balking and reneging customers) and threshold strategies

Large deviations analysis for the M/H2/n+MM/H_2/n + M queue in the Halfin-Whitt regime

We consider the FCFS $M/H_2/n + M$ queue in the Halfin-Whitt heavy traffic regime. It is known that the normalized sequence of steady-state queue length distributions is tight and converges weakly to a limiting random variable W. However, those works only describe W implicitly as the invariant measure of a complicated diffusion. Although it was proven by Gamarnik and Stolyar that the tail of W is sub-Gaussian, the actual value of $\lim_{x \rightarrow \infty}x^{-2}\log(P(W >x))$ was left open. In subsequent work, Dai and He conjectured an explicit form for this exponent, which was insensitive to the higher moments of the service distribution. We explicitly compute the true large deviations exponent for W when the abandonment rate is less than the minimum service rate, the first such result for non-Markovian queues with abandonments. Interestingly, our results resolve the conjecture of Dai and He in the negative. Our main approach is to extend the stochastic comparison framework of Gamarnik and Goldberg to the setting of abandonments, requiring several novel and non-trivial contributions. Our approach sheds light on several novel ways to think about multi-server queues with abandonments in the Halfin-Whitt regime, which should hold in considerable generality and provide new tools for analyzing these systems

The Impact of Mobile Order Ahead Apps on QSR Queuing

Order ahead mobile apps are becoming increasingly popular at Quick Serve Restaurants. These apps allow customers skip the line when arriving at the store. We investigate the hybrid queuing system created by these applications. We define an overall structure for the hybrid queuing system. Using discrete event simulation, we examine the impact these apps can have on system performance. Our analysis indicates that overall, the mobile application increases the efficiency of the system as a whole. By completing food preparation before the customer arrives the total waiting time for all customers is reduced. The walk-in customer also sees the benefits as overall system efficiency improves although they may feel slighted as customers arrive and skip the line