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

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

Rate stability and output rates in queueing networks with shared resources

Motivated by a variety of applications in information and communication systems, we consider queueing networks in which the service rate at each of the individual nodes depends on the state of the entire system. The asymptotic behaviour of this type of networks is fundamentally different from classical queueing networks, where the service rate at each node is usually assumed to be independent of the state of the other nodes. We study the per-node rate stability and output rates for a general class of feed-forward queueing networks with a general capacity allocation function. More specifically, we derive necessary conditions of per-node rate stability, and give bounds for the per-node output rate and asymptotic growth rates, under mild assumptions on the allocation function. For a set of parallel nodes, we further prove the convergence of the output rates and give a sharp characterization of the per-node rate stability. The results provide new intuition and fundamental insight in the stability and throughput behavior of queueing networks with shared resources

Demand-point constrained EMS vehicle allocation problems for regions with both urban and rural areas

Governments deal with increasing health care demand and costs, while budgets are tightened. At the same time, ambulance providers are expected to deliver high-quality service at affordable cost. Maximum reliability and minimal availability models guarantee a minimal performance level at each demand point, in contrast to the majority of facility location and allocation methods that guarantee a minimal

Heavy-traffic limits for Polling Models with Exhaustive Service and non-FCFS Service Order Policies

We study cyclic polling models with exhaustive service at each queue under a variety of non-FCFS local service orders, namely Last-Come-First-Served (LCFS) with and without preemption, Random-Order-of-Service (ROS), Processor Sharing (PS), the multi-class priority scheduling with and without preemption, Shortest-Job-First (SJF) and the Shortest Remaining Processing Time (SRPT) policy. For each of these policies, we rst express the waiting-time distributions in terms of intervisit-time distributions. Next, we use these expressions to derive the asymptotic waiting-time distributions under heavy-trac assumptions, i.e., when the system tends to saturate. The results show that in all cases the asymptotic wait