Waiting times in queueing networks with a single shared server

We study a queueing network with a single shared server that serves the queues in a cyclic order. External customers arrive at the queues according to independent Poisson processes. After completing service, a customer either leaves the system or is routed to another queue. This model is very generic and finds many applications in computer systems, communication networks, manufacturing systems, and robotics. Special cases of the introduced network include well-known polling models, tandem queues, systems with a waiting room, multi-stage models with parallel queues, and many others. A complicating factor of this model is that the internally rerouted customers do not arrive at the various queues according to a Poisson process, causing standard techniques to find waiting-time distributions to fail. In this paper we develop a new method to obtain exact expressions for the Laplace-Stieltjes transforms of the steady-state waiting-time distributions. This method can be applied to a wide variety of models which lacked an analysis of the waiting-time distribution until now

Towards a unifying theory on branching-type polling systems in heavy traffic

For a broad class of polling models the evolution of the system at specific embedded polling instants is known to constitute a multi-type branching process (MTBP) with immigration. In this paper we derive heavy-traffic limits for general MTBP-type of polling models. The results generalize and unify many known results on the waiting times in polling systems in heavy traffic, and moreover, lead to new exact results for classical polling models that have not been observed before. To demonstrate the usefulness of the results, we derive closed-form expressions for the LST of the waiting-time distributions for models with cyclic globally-gated polling regimes, and for cyclic polling models with general branching-type service policies. As a by-product, our results lead to a number of asymptotic insensitivity properties, providing new fundamental insights in the behavior of polling models

A queueing theory approach to Pareto-optimal bags-of-tasks scheduling on clouds

Cloud hosting services offer computing resources which can scale along with the needs of users. When access to data is limited by the network capacity this scalability also becomes limited. To investigate the impact of this limitation we focus on bags{of{tasks where task data is stored outside the cloud and has to be transferred across the network before task execution can commence. The existing bags-of-tasks estimation tools are not able to provide accurate estimates in such a case. We introduce a queuing{network inspired model which successfully models the limited network resources. Based on the Mean{Value Analysis of this model we derive an efficient procedure that results with an estimate of the makespan and the executions costs for a given configuration of cloud virtual machines. We compare the calculated Pareto set with measurements performed in a number of experiments for real-world bags-of-tasks and validate the proposed model and the accuracy of the estimated configurations

Fluid Approximation of a Call Center Model with Redials and Reconnects

In many call centers, callers may call multiple times. Some of the calls are re-attempts after abandonments (redials), and some are re-attempts after connected calls (reconnects). The combination of redials and reconnects has not been considered when making staffing decisions, while ignoring them will inevitably lead to under- or overestimation of call volumes, which results in improper and hence costly staffing decisions. Motivated by this, in this paper we study call centers where customers can abandon, and abandoned customers may redial, and when a customer finishes his conversation with an agent, he may reconnect. We use a fluid model to derive first order approximations for the number of customers in the redial and reconnect orbits in the heavy traffic. We show that the fluid limit of such a model is the unique solution to a system of three differential equations. Furthermore, we use the fluid limit to calculate the expected total arrival rate, which is then given as an input to the Erlang A model for the purpose of calculating service levels and abandonment rates. The performance of such a procedure is validated in the case of single intervals as well as multiple intervals with changing parameters

Polling models with multi-phase gated service

In this paper we introduce and analyze a new class of service policies called multi-phase gated service. This policy is a generalization of the classical single-phase and two-phase gated policies and works as follows. Each customer that arrives at queue i will have to wait K_i cycles before it receives service. The aim of this policy is to provide an interleaving scheme to avoid monopolization of the system by heavily loaded queues, by choosing the proper values of interleaving levels Ki. In this paper, we analyze the effectiveness of the interleaving scheme on the queueing behavior of the system, and consider the problem of identifying the proper combination of interleaving levels (K_1,...,K_N) that minimizes a weighted sum of the mean waiting times at each of the N queues. Obviously, the proper choice of the interleaving levels is most critical when the system is heavily loaded. For this reason, we to obtain closed-form expressions for the asymptotic waiting-time distributions in heavy trafficc, and use these expressions to derive simple heuristics for approximating the optimal interleaving scheme. Numerical results with simulations demonstrate that the accuracy of these approximations is extremely high

Single-leg choice-based revenue management: a robust optimisation approach

A popular trend in revenue management captures the behaviour of customers that choose between different available products. The provided solution methods assume that there is no uncertainty in the parameters of the model. However, in practice the parameters may be uncertain, e.g., because of estimation errors. A relatively recent field of optimisation that takes into account uncertainty in the optimisation procedure is robust optimisation. Robust optimisation methods provide solutions where the worst-case scenario is optimised, taking into account uncertainty in parameters. This paper studies a robust optimisation approach to single-leg choice-based revenue management based on Talluri and van Ryzin (Manag Sci 50:15–33, 2004) and Sierag et al (Eur J Oper Res 246:170–185, 2015). The problem is modelled as a Markov decision process and solved using dynamic programming. This paper uses ϕ-divergence uncertainty sets to model the probability vectors of general choice-models. Novel robust optimisation techniques are applied to the dynamic program, taking into account uncertainty in the parameters. An important yet surprising insight from the numerical results is that the robust solution method performs better for smaller inventory than for larger inventory. Moreover, the robust solution method shows great performance when knowledge on cancellation behaviour is lacking: on average the expected reward then improves by 2.5–3.25 per cent

A machine learning approach to itinerary-level booking prediction in competitive airline markets

Demand forecasting is extremely important in revenue management. After all, it is one of the inputs to an optimisation method which aim is to maximize revenue. Most, if not all, forecasting methods use historical data to forecast the future, disregarding the "why". In this paper, we combine data from multiple sources, including competitor data, pricing, social media, safety and airline reviews. Next, we study five competitor pricing movements that, we hypothesize, affect customer behavior when presented a set of itineraries. Using real airline data for ten different OD-pairs and by means of Extreme Gradient Boosting, we show that customer behavior can be categorized into price-sensitive, schedule-sensitive and comfort ODs. Through a simulation study, we show that this model produces forecasts that result in higher revenue than traditional, time series forecasts