Yoav Kerner

Ben-Gurion University of the Negev | bgu · Department of Industrial Engineering and Management

We derive the mean waiting times in an M/G/1 priority queue when the decision who receives the current completed service (production) is determined at the end of the service period. We consider two variations of this scheme. The first is when the server works only when customers are present, while the second is when the server works on a nonstop ba...

Quantitative business process analysis is a powerful approach for analysing timing properties of a business process, such as the expected waiting time of customers or the utilization rate of resources. Multiple techniques are available for quantitative business process analysis, which all have their own advantages and disadvantages. This paper pres...

In standard queues, when there are waiting customers, service completions are followed by service commencements. In retrial queues, this is not the case. In such systems, customers try to receive service at a time of their choosing, or the server seeks the next customer for a non-negligible time. In this note, we consider a hybrid model with both a...

In this paper, we provide a new approach to model the inter-departure times distribution in a PH/G/1 queue. This approach enables to further model the inter-departure times distribution in more general queues as well. Initially, we propose to express the Laplace–Stieltjes transform (LST) of inter-departure times in PH/G/1 queues by exploiting the p...

We consider an M / G / 1 queue in which the customers, while waiting in line, may renege from it. We show the Nash equilibrium profile among customers and show that it is defined by two sequences of thresholds. For each customer, the decision is based on the observed past (which determines from what sequence the threshold is taken) and the observed...

Objectives: Intra-abdominal adhesions may result in an increased risk of major complications in case of a repeated cesarean section, such as bladder and bowel injury, hemorrhage, infection, and hysterectomy. In an attempt to predict intra-abdominal adhesions before a repeated cesarean delivery, we suggest the use of a novel technique employing a s...

We consider a queueing facility where customers decide when to arrive. All customers have the same desired arrival time (w.l.o.g. time zero). There is one server, and the service times are independent and exponentially distributed. The total number of customers that demand service is random, and follows the Poisson distribution. Each customer wishe...

An analytical model of Human-Robot (H-R) coordination is presented for a Human-Robot system executing a collaborative task in which a high level of synchronization among the agents is desired. The influencing parameters and decision variables that affect the waiting time of the collaborating agents were analyzed. The performance of the model was ev...

We consider a queueing facility where customers decide when to arrive. All customers have the same desired arrival time (w.l.o.g.\ time zero). There is one server, and the service times are independent and exponentially distributed. The total number of customers that demand service is random, and follows the Poisson distribution. Each customer wish...

In many real-life queueing systems, a customer may balk upon arrival at a queueing system, but other customers become aware of it only at the time the balking customer was to start service. Naturally, the balking is an outcome of the queue length, and the decision is based on a threshold. Yet the inspected queue length contains customers who balked...

In many real life queueing systems, a customer may balk upon arrival to a queueing system, but other customers become aware of it only at the time the balking customer was to start service. Naturally, the balking is an outcome of the queue length, and the decision is based on a threshold. Yet, the inspected queue length contains customers who balke...

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We consider a queueing facility where customers must decide when to arrive. All customers have the same desired arrival time (w.l.o.g. time zero). There is one server, and the service times are independent and exponentially distributed. The total number of customers that demand service is random, and follows the Poisson distribution. Each customer...

This paper studies an M/G/1 production system serving several customer classes. We show that the Multilevel Rationing (MR) policy, that has been shown to be optimal in the M/M/1 case is not optimal in general. We propose another policy, which we call the extended MR (EMR). The EMR policy exploits the information on the number of all waiting custome...

We consider the output processes of some elementary queueing models such as the M/M/1/K queue and the M/G/1 queue. An important performance measure for these counting processes is their variance curve v(t), which gives the variance of the number of customers in the time interval [0, t]. Recent work has revealed some non-trivial properties dealing w...

We show that overshoots over Erlang random variables give rise to a natural generalization of the stationary excess operator and its iterates. The new operators can be used to derive expansions for the expectation E g ( X ) of a non-negative random variable, similar to Taylor-like expansions encountered when studying stationary excess operators.

We consider queueing output processes of some elementary queueing models such as the M/M/1/K queue and the M/G/1 queue. An important performance measure for these counting processes is their variance curve, indicating the variance of the number of served customers over a time interval. Recent work has revealed some non-trivial properties dealing wi...

An analytical model of Human-Robot (H-R) coordination is presented for a Human-Robot system executing a collaborative task in which a high level of synchronization among the agents is desired. The influencing parameters and decision variables that affect the waiting time of the collaborating agents were analyzed. The performance of the model was ev...

Services such as FedEx charge up-front fees but reimburse customers for delays. However, lead-time pricing studies ignore such delay refunds. This paper contributes to filling this gap. It studies revenue-maximizing tariffs that depend on realized lead times for a provider serving multiple time-sensitive customer types. We relax two key assumptions...

We study the mean and the distribution of the time elapsing between two consecutive departures from the stationary M/G/s queue given the number of customers left behind by the first departure is equal to n. It is conjectured that if the failure rate of the service time distribution is increasing (decreasing), then (i) the limit of the mean conditio...

We study the customers' Nash equilibrium behavior in a single server observable queue with Poisson arrivals and general service times. Each customer takes a single decision upon arrival: to join or not to join. Furthermore, future regrets are not allowed. The customers are homogenous with respect to their linear waiting cost and the reward associat...

This paper shows that in the G/M/1 queueing model, conditioning on a busy server, the age of the inter-arrival time and the number of customers in the queue are independent. The same is the case when the age is replaced by the residual inter-arrival time or by its total value. Explicit expressions for the conditional density functions, as well as s...

In most decision models dealing with unobservable stochastic con- gested environments, one looks for a (Nash) equilibrium behavior among customers. This is a strategy that if adopted by all, then under the resulting steady-state conditions, the best response for an individ- ual is to adopt this strategy too. The purpose of this paper is to look for...

The Price of Anarchy (PoA) is the ratio of optimal and equilibrium social welfare. We consider the most fundamental queueing model in- volving customers' decisions, as studied by Naor (1969). We show that the PoA has an odd behavior as a function of the system's congestion. In particular, when the ratio of the potential arriving rate and the ser- v...

We show that in the stationary M=G=1 queue, if the ser- vice time distribution is with increasing (decreasing) failure rate (IFR (DFR)), then (a) The distribution of the number of customers in the system is also IFR (DFR), (b) The conditional distribution of the re- maining service time given the number of customers in the system is also IFR (DFR)...

We study a single server queueing system with general service time distribution and memoryless inter-arrival times. The arrival rate is not constant but varies with the number of customers in the system. A recursive formula for the conditional distribution of the remaining service time given the queue length is derived for an arbitrary epoch. It is...

The intuition while observing the economy of queueing systems, is that one’s motivation to join the system, decreases with its level of congestion. Here we present a queueing model where sometimes the opposite is the case. The point of departure is the standard first-come first-served single server queue with Poisson arrivals. Customers commence se...

We present a method for the analysis of queueing output processes that is based on an embedding of the output process in a renewal-reward process in which the renewal periods are busy cycles and the rewards represent the numbers of customers served during busy cycles. Our method yields an approximation for the variance curve that is asymptotically...

We revisit a classic result by D.J. Daley regarding the variance curve of outputs from the stationary M/G/1 queue. We use this result to obtain the linear asymptote of the variance curve for both the stationary system and the system starting with an arbitrary initial conditions. We also obtain the limiting covariance of the number of arrivals and t...