Consider a network of n single-server queues where tasks arrive independently at each server at rate λ_n. The servers are connected by a graph that is resampled at rate μ_n in a way that is symmetric with respect to the servers, and each task is dispatched to the shortest queue in the graph neighborhood where it appears. We aim to gain insight in the impact of the dynamic network structure on the load balancing dynamics in terms of the occupancy process which describes the empirical distribution of the number of tasks across the servers. This process evolves on the underlying dynamic graph, and its dynamics depend on the number of tasks at each individual server and the neighborhood structure of the graph. We establish that this dependency disappears in the limit as n →∞ when λ_n / n → λ and μ_n →∞, and prove that the limit of the occupancy process is given by a system of differential equations that depends solely on λ and the limiting degree distribution of the graph. We further show that the stationary distribution of the occupancy process converges to an equilibrium of the differential equations, and derive properties of this equilibrium that reflect the impact of the degree distribution. Our focus is on truly sparse graphs where the maximum degree is uniformly bounded across n, which is natural in load balancing systems.

Programmable packet schedulers provide great flexibility in the ordering of packet transmission. They allow network operators to optimize crucial performance metrics, such as Flow Completion Time (FCT), using strategies that adapt to changes in the characteristics of incoming traffic. A challenge in programming these devices is that they are severely limited in registers, memory, and control flow operations. The popular scheduling strategy Push-In First-Out (PIFO), for example, cannot be straightforwardly implemented because it relies on sorting packets, which is difficult to implement at line speed on current hardware. Fixed-priority approximations of PIFO, like SP-PIFO and AIFO, do have hardware implementations but generally still do not scale well in, for example, the number of memory cells being used. This paper introduces a new PIFO approximation strategy, Exp-PIFO, which prioritizes packets based on adaptive exponential prioritization criteria, called exponential bins. Exp-PIFO approximates the behavior of PIFO using only two memory cells to keep track of its state and uses a lookup table to avoid a complex control flow. We initially expected our improvement in memory and computation to come at a cost w.r.t. FCT performance compared to PIFO and its existing approximations. However, our empirical evaluation shows that Exp-PIFO sometimes even outperforms strict PIFO. We provide an explanation for this behavior and demonstrate the practical feasibility of Exp-PIFO through a proof-of-concept implementation on an Intel Tofino switch, which uses significantly less memory than comparable implementations of SP-PIFO and AIFO.

We use bipartite graphs to model compatibility constraints that arise between tasks and servers in data centers, cloud computing systems and content delivery networks. We prove that servers with skewed graph neighborhoods saturate with tasks in a limiting regime. The neighborhood of a server is skewed if it contains a diverging number of dispatchers with uniformly bounded degrees.

Consider a system of identical server pools where tasks with exponentially distributed service times arrive as a time-inhomogenenous Poisson process. An admission threshold is used in an inner control loop to assign incoming tasks to server pools while, in an outer control loop, a learning scheme adjusts this threshold over time to keep it aligned with the unknown offered load of the system. In a many-server regime, we prove that the learning scheme reaches an equilibrium along intervals of time where the normalized offered load per server pool is suitably bounded, and that this results in a balanced distribution of the load. Furthermore, we establish a similar result when tasks with Coxian distributed service times arrive at a constant rate and the threshold is adjusted using only the total number of tasks in the system. The novel proof technique developed in this paper, which differs from a traditional fluid limit analysis, allows to handle rapid variations of the first learning scheme, triggered by excursions of the occupancy process that have vanishing size. Moreover, our approach allows to characterize the asymptotic behavior of the system with Coxian distributed service times without relying on a fluid limit of a detailed state descriptor.

Cellular networks are carefully planned to provide sufficient coverage and capacity under normal circumstances. However, in emergency scenarios like floodings, wildfires, earthquakes or even terrorist attacks, part of the network may no longer be operational while at the same time a traffic hotspot may occur as a consequence of such an event. In such scenarios it is of utmost importance to quickly restore wireless coverage with sufficient capacity. To achieve this goal, we consider the dynamic deployment of drone-mounted base stations and propose a data-driven algorithm which optimizes the positions of the drone base stations based on measurement values that are readily available. We demonstrate that the use of well-positioned drones yields significant performance improvements and that the proposed method outperforms relevant benchmarks and is able to achieve close to optimal performance. For example, in rural scenarios we may observe in certain cases a twofold reduction in the fraction of failed calls compared to a pre-planned deployment of drones, and an even greater improvement over a setting without drones.

Modern service systems, like cloud computing platforms or data center environments, commonly face a high degree of heterogeneity. This heterogeneity is not only caused by different server speeds but also, by binding task-server relations that must be taken into account when assigning incoming tasks. Unfortunately, there are hardly any theoretical performance guarantees as these systems do not fall within the typical supermarket modeling framework which heavily relies on strong symmetry and homogeneity assumptions. In “Heavy-traffic universality of redundancy systems with assignment constraints,” Cardinaels, Borst, and van Leeuwaarden provide insight in the performance of these systems operating under redundancy scheduling policies. Surprisingly, when experiencing high demand, these systems exhibit state space collapse and can achieve a similar level of resource pooling and performance as a fully flexible system, even subject to quite strict task-server constraints.

Under normal circumstances wireless cellular networks provide adequate coverage and capacity. However in case of site failures, due to for example an earthquake or flooding, it is important to quickly resolve the resulting coverage and/or capacity problem. To achieve this goal, we investigate the joint use of dynamically deployed drone-mounted base stations (DBSs) and a cell outage compensation (COC) mechanism. With COC the surrounding, still operational, cells adjust their configuration to mitigate the performance degradation. We demonstrate that these two approaches can work well together and complement each other in the sense that while COC on its own is usually unable to restore the performance to its original level, it can help to significantly reduce the number of DBSs required to achieve this. In particular, in urban scenarios we observe a reduction in the number of DBSs to be deployed by up to 40%.

We consider random-access networks where nodes represent servers with a queue and can be either active or inactive. A node deactivates at unit rate, while it activates at a rate that depends on its queue length, provided none of its neighbors is active. We consider arbitrary bipartite graphs in the limit as the initial queue lengths become large and identify the transition time between the two states where one half of the network is active and the other half is inactive. The transition path is decomposed into a succession of transitions on complete bipartite subgraphs. We formulate a randomized greedy algorithm that takes the graph as input and gives as output the set of transition paths the network is most likely to follow. Along each path we determine the mean transition time and its law on the scale of its mean. Depending on the activation rates, we identify three regimes of behavior.

We establish an explicit multi-dimensional state space collapse (SSC) for parallel-processing systems with arbitrary compatibility constraints between servers and job types. This breaks major new ground beyond the SSC results and queue length asymptotics in the literature which are largely restricted to complete resource pooling (CRP) scenarios where the steady-state queue length vector concentrates around a line in heavy traffic. The multi-dimensional SSC that we establish reveals heavy-traffic behavior which is also far more tractable than the pre-limit queue length distribution, yet exhibits a fundamentally more intricate structure than in the one-dimensional case.

Wireless communication networks provide a critical infrastructure, particularly in emergency situations due to disruptive events such as natural disasters or terrorist attacks. However, in these kinds of scenarios part of the network may no longer be operational and a traffic hotspot may emerge, which may result in coverage and/or capacity issues. Deploying self-steering drone-mounted base stations offers a potential method to quickly restore coverage and/or provide capacity relief in such situations, but appropriate positioning is crucial in order for a drone base station to be truly effective. Motivated by that challenge, we propose a data-driven algorithm to optimize the position of a drone base station in a scenario with a site failure and emergence of a traffic hotspot. We demonstrate that the use of a drone, when properly positioned, yields significant performance gains, and that our algorithm outperforms benchmark mechanisms in a wide range of scenarios. In addition, we show that our algorithm is able to find a near-optimal position for the drone in a reasonable amount of time, and even has the ability to track the optimal position in case of a moving hotspot.

Intelligent Transportation Systems (ITSs) are envisioned to play a critical role in improving traffic flow and reducing congestion, which is a pervasive issue impacting urban areas around the globe. Rapidly advancing vehicular communication and edge cloud computation technologies provide key enablers for smart traffic management. However, operating viable real-time actuation mechanisms on a practically relevant scale involves formidable challenges, e.g., policy iteration and conventional Reinforcement Learning (RL) techniques suffer from poor scalability due to state space explosion. Motivated by these issues, we explore the potential for Deep Q-Networks (DQN) to optimize traffic light control policies. As an initial benchmark, we establish that the DQN algorithms yield the "thresholding" policy in a single-intersection. Next, we examine the scalability properties of DQN algorithms and their performance in a linear network topology with several intersections along a main artery. We demonstrate that DQN algorithms produce intelligent behavior, such as the emergence of "greenwave" patterns, reflecting their ability to learn favorable traffic light actuations.

In this paper we establish a necessary and sufficient stability condition for a stochastic ring network. Such networks naturally appear in a variety of applications within communication, computer, and road traffic systems. They typically involve multiple customer types and some form of priority structure to decide which customer receives service. These two system features tend to complicate the issue of identifying a stability condition, but we demonstrate how the ring topology can be leveraged to solve the problem.

Consider a system of $n$ single-server queues where tasks arrive at each server in a distributed fashion. A graph is used to locally balance the load by dispatching every incoming task to one of the shortest queues in the neighborhood where the task appears. In order to globally balance the load, the neighborship relations are constantly renewed by resampling the graph at rate $\mu_n$ from some fixed random graph law. We derive the fluid limit of the occupancy process as $n \to \infty$ and $\mu_n \to \infty$ when the resampling procedure is symmetric with respect to the servers. The maximum degree of the graph may remain bounded as $n$ grows and the total number of arrivals between consecutive resampling times may approach infinity. The fluid limit only depends on the random graph laws through their limiting degree distribution and can be interpreted as a generalized power-of-$(d + 1)$ scheme where $d$ is random and has the limiting degree distribution. We use the fluid limit to obtain valuable insights into the performance impact and optimal design of sparse dynamic graphs with a bounded average degree. In particular, we establish a phase transition in performance when the probability that a server is isolated switches from zero to positive, and we show that performance improves as the degree distribution becomes more concentrated.

The anticipated launch of fully autonomous vehicles presents an opportunity to develop and implement novel traffic management systems. Intersections are one of the bottlenecks for urban traffic, and thus offer tremendous potential for performance improvements of traffic flow if managed efficiently. Platoon-forming algorithms, in which vehicles are grouped together with short inter-vehicular distances just before arriving at an intersection at high speed, seem particularly promising in this aspect. In this work, we present an intersection access control system based on platoon-forming for heterogeneous autonomous traffic. The heterogeneity of traffic arises from vehicles with different acceleration capabilities and safety constraints. We focus on obtaining computationally fast and interpretable closed-form expressions for safe and efficient vehicle trajectories that lead to platoon formation, and show that these trajectories are solutions to certain classes of optimisation problems. Additionally, we conduct a numerical study to obtain approximations for intersection capacity as a result of such platoon formation.

Reliable mobile communications is of critical importance, and should be maintained even in case of extremely crowded events or emergency scenarios. In such scenarios the deployment of drone-mounted base stations offers an agile and cost-efficient way to sustain coverage and/or provide capacity relief. In this paper we develop an analytical method to estimate the blocking and coverage probabilities of drone-assisted cellular networks using information that is readily available from network planning tools. We demonstrate how this method can be used to determine the minimum required number of drones and their corresponding locations for a given target performance level.

The present paper is concerned with the stationary workload of queues with heavy-tailed (regularly varying) characteristics. We adopt a transform perspective to illuminate a close connection between the tail asymptotics and heavy-traffic limit in infinite-variance scenarios. This serves as a tribute to some of the pioneering results of J.W. Cohen in this domain. We specifically demonstrate that reduced-load equivalence properties established for the tail asymptotics of the workload naturally extend to the heavy-traffic limit.

We present diffusion limits for a queuing system with n parallel servers with concurrent service capabilities. The diffusion limits are established in the many-server heavy-traffic regime where ( 1 − ρ n ) n α → β as n → ∞, for α ∈ ( 0 , ∞ ) ∖ { 1 / 2 } and ρ n a notion of normalized system load. This encompasses the so-called sub-Halfin-Whitt, super-Halfin-Whitt, non-degenerate slowdown, and super-slowdown regimes. The diffusion limits are universal in that they depend only on whether α < 1 / 2 or α > 1 / 2 and do not depend on specific values of α and β in both cases.

In this paper, we study the performance of a bipartite network in which customers arrive at the nodes of the network, but not all nodes are able to serve their customers at all times. Each node can be either active or inactive, and two nodes connected by a bond cannot be active simultaneously. This situation arises in wireless random-access networks where, due to destructive interference, stations that are close to each other cannot use the same frequency band. We consider a model where the network is bipartite, the active nodes switch themselves off at rate 1 and the inactive nodes switch themselves on at a rate that depends on time and on which half of the bipartite network they are in. An inactive node cannot become active when one of the nodes it is connected to by a bond is active. The switching protocol allows the nodes to share activity among each other. In the limit as the activation rate becomes large, we compute the crossover time between the two states where one-half of the network is active and the other half is inactive. This allows us to assess the overall activity of the network depending on the switching protocol. Our results make use of the metastability analysis for hard-core interacting particle models on finite bipartite graphs derived in an earlier paper. They are valid for a large class of bipartite networks, subject to certain assumptions. Proofs rely on a comparison with switching protocols that are not time varying, through coupling techniques.

In this survey we provide an overview of recent advances on scalable load balancing schemes which provide favorable delay performance and yet require minimal implementation overhead. The basic load balancing scenario involves a single dispatcher where tasks arrive that must immediately be forwarded to one of N single-server queues. The join-the-shortestqueue (JSQ) policy yields vanishing delays as N grows large, as in a centralized queuing arrangement, but involves a prohibitive communication burden. In contrast, JSQ(d) schemes that assign an incoming task to a server with the shortest queue among d servers selected uniformly at random require little communication, but lead to constant delays. In order to examine this fundamental trade-off between delay performance and implementation overhead, we discuss a body of recent research on JSQ(d(N)) schemes in which the diversity parameter d(N) depends on N and investigate the growth rate of d(N) required to match the optimal JSQ performance on fluid and diffusion scales. Stochastic coupling techniques and scaling limits play an instrumental role in establishing this asymptotic optimality. We demonstrate how this methodology carries over to infinite-server settings, finite buffers, multiple dispatchers, servers arranged on graph topologies, and token-based load balancing schemes such as join-the-idle-queue (JIQ), thus providing a broad overview of the main trends in the field.