Stability of Parallel Server Systems

A parallel server system is a queueing system in which jobs are routed upon their arrivals to one of several buffers, each handled by a different server. The main operational and theoretical problem in such systems is to find an efficient routing policy that maximizes their throughput (or minimizes waiting times). The paper “Stability of Parallel Server Systems” considers a large class of routing policies, which includes the most prevalent policies studies in the literature, under the assumption that routing errors may occur because ofincomplete information about the state of the system at decision epochs. The stability region for this class of policies is studied as a function of the error probability, and it is shown that the standard stability condition, namely, that the traffic intensity is smaller than one, does not guarantee that the system is stable.

Minimizing Mean Response Time In Batch-Arrival Non-Observable Systems With Single-Server FIFO Queues Operating In Parallel

Consideration is given to a dispatching system, where jobs, arriving in batches, cannot be stored and thus must be immediately routed to single-server FIFO queues operating in parallel. The dispatcher can memorize its routing decisions but at any time instant does not have any system's state information. The only information available is the batch/job size and inter-arrival time distributions, and the servers' service rates. Under these conditions, one is interested in the routing policies which minimize the job's long-run mean response time. The single-parameter routing policy is being proposed which, according to the numerical experiments, outperforms best routing rules known by now for non-observable dispatching systems: probabilistic and deterministic. Both the batch-wise and job-wise assignments are studied. Extension to systems with unreliable servers is also addressed.

Size-Based Routing Policies: Non-Asymptotic Analysis and Design of Decentralized Systems

Size-based routing policies are known to perform well when the variance of the distribution of the job size is very high. We consider two size-based policies in this paper: Task Assignment with Guessing Size (TAGS) and Size Interval Task Assignment (SITA). The latter assumes that the size of jobs is known, whereas the former does not. Recently, it has been shown by our previous work that when the ratio of the largest to shortest job tends to infinity and the system load is fixed and low, the average waiting time of SITA is, at most, two times less than that of TAGS. In this article, we first analyze the ratio between the mean waiting time of TAGS and the mean waiting time of SITA in a non-asymptotic regime, and we show that for two servers, and when the job size distribution is Bounded Pareto with parameter α=1, this ratio is unbounded from above. We then consider a system with an arbitrary number of servers and we compare the mean waiting time of TAGS with that of Size Interval Task Assignment with Equal load (SITA-E), which is a SITA policy where the load of all the servers are equal. We show that in the light traffic regime, the performance ratio under consideration is unbounded from above when (i) the job size distribution is Bounded Pareto with parameter α=1 and an arbitrary number of servers as well as (ii) for Bounded Pareto distributed job sizes with α∈(0,2)\{1} and the number of servers tends to infinity. Finally, we use the result of our previous work to show how to design decentralized systems with quality of service constraints.

Electric Vehicle Routing with Public Charging Stations

We introduce the electric vehicle routing problem with public-private recharging strategy in which vehicles may recharge en route at public charging infrastructure as well as at a privately-owned depot. To hedge against uncertain demand at public charging stations, we design routing policies that anticipate station queue dynamics. We leverage a decomposition to identify good routing policies, including the optimal static policy and fixed-route-based rollout policies that dynamically respond to observed queues. The decomposition also enables us to establish dual bounds, providing a measure of goodness for our routing policies. In computational experiments using real instances from industry, we show the value of our policies to be within 10% of a dual bound. Furthermore, we demonstrate that our policies significantly outperform the industry-standard routing strategy in which vehicle recharging generally occurs at a central depot. Our methods stand to reduce the operating costs associated with electric vehicles, facilitating the transition from internal-combustion engine vehicles.

Load-Optimization in Reconfigurable Networks

Emerging reconfigurable data centers introduce the unprecedented flexibility in how the physical layer can be programmed to adapt to current traffic demands. These reconfigurable topologies are commonly hybrid, consisting of static and reconfigurable links, enabled by e.g. an Optical Circuit Switch (OCS) connected to top-of-rack switches in Clos networks. Even though prior work has showcased the practical benefits of hybrid networks, several crucial performance aspects are not well understood. In this paper, we study the algorithmic problem of how to jointly optimize topology and routing in reconfigurable data centers with a known traffic matrix, in order to optimize a most fundamental metric, maximum link load. We chart the corresponding algorithmic landscape by investigating both un-/splittable flows and (non-)segregated routing policies. We moreover prove that the problem is not submodular for all these routing policies, even in multi-layer trees, where a topological complexity classification of the problem reveals that already trees of depth two are intractable. However, networks that can be abstracted by a single packet switch (e.g., nonblocking Fat-Tree topologies) can be optimized efficiently, and we present optimal polynomialtime algorithms accordingly. We complement our theoretical results with trace-driven simulation studies, where our algorithms can significantly improve the network load in comparison to the state of the art.

Convolutional LSTM models to estimate network traffic

Network utilisation efficiency can, at least in principle, often be improved by dynamically re-configuring routing policies to better distribute ongoing large data transfers. Unfortunately, the information necessary to decide on an appropriate reconfiguration—details of on-going and upcoming data transfers such as their source and destination and, most importantly, their volume and duration—is usually lacking. Fortunately, the increased use of scheduled transfer services, such as FTS, makes it possible to collect the necessary information. However, the mere detection and characterisation of larger transfers is not sufficient to predict with confidence the likelihood a network link will become overloaded. In this paper we present the use of LSTM-based models (CNN-LSTM and Conv-LSTM) to effiectively estimate future network traffic and so provide a solid basis for formulating a sensible network configuration plan.

A Joint Comparative Analysis of Routing Heuristics and Paperless Picking Technologies Using Simulation and Data Envelopment Analysis

Recent literature demonstrates that warehouse order picking performance is reflected in the logistics performance of downstream retailers. Warehouse solutions and policies significantly contribute to the improvement of distribution and delivery to retailers. This paper therefore reports an analysis of the joint performance of routing policies and picking technologies, and provides insights into the best ways to combine routing strategies and paperless solutions in order to optimize cost efficiency. We follow a multistage approach that combines mixed integer linear programming algorithms, data envelopment analysis (DEA), and ranking and selection. The results show that traversal-voice picking and midpoint-voice picking combinations are equally distributed over the most efficient subsets and that superior technology can enhance picking efficiency only to a certain level. The study provides guidelines for logistics managers on ways to combine warehouse solutions and policies in order to better streamline the operations. It offers an original framework to analyze the joint performance of picking routing and picking solutions by considering the effect of picking errors.