Shortest Expected Delay Routing for Erlang Servers

The queueing problem with a Poisson arrival stream and two identical Erlang servers is analysed for the queueing discipline based on shortest expected delay. This queueing problem may be represented as a random walk on the integer grid in the first quadrant of the plane. In the paper it is shown that the equilibrium distribution of this random walk can be written as a countable linear combination of product forms. This linear combination is constructed in a compensation procedure. In this case the compensation procedure is essentially more complicated than in other cases where the same idea was exploited. The reason for the complications is that in this case the boundary consists of several layers which in turn is caused by the fact that transitions starting in inner states are not restricted to end in neighbouring states. Good starting solutions for the compensation procedure are found by solving the shortest expected delay problem with the same service distributions but with instantaneous jockeying. It is also shown that the results can be used for an efficient computation of relevant performance criteria

Steady-state analysis of shortest expected delay routing

We consider a queueing system consisting of two non-identical exponential servers, where each server has its own dedicated queue and serves the customers in that queue FCFS. Customers arrive according to a Poisson process and join the queue promising the shortest expected delay, which is a natural and near-optimal policy for systems with non-identical servers. This system can be modeled as an inhomogeneous random walk in the quadrant. By stretching the boundaries of the compensation approach we prove that the equilibrium distribution of this random walk can be expressed as a series of product-forms that can be determined recursively. The resulting series expression is directly amenable for numerical calculations and it also provides insight in the asymptotic behavior of the equilibrium probabilities as one of the state coordinates tends to infinity.Comment: 41 pages, 13 figure

Delay versus Stickiness Violation Trade-offs for Load Balancing in Large-Scale Data Centers

Most load balancing techniques implemented in current data centers tend to rely on a mapping from packets to server IP addresses through a hash value calculated from the flow five-tuple. The hash calculation allows extremely fast packet forwarding and provides flow `stickiness', meaning that all packets belonging to the same flow get dispatched to the same server. Unfortunately, such static hashing may not yield an optimal degree of load balancing, e.g., due to variations in server processing speeds or traffic patterns. On the other hand, dynamic schemes, such as the Join-the-Shortest-Queue (JSQ) scheme, provide a natural way to mitigate load imbalances, but at the expense of stickiness violation. In the present paper we examine the fundamental trade-off between stickiness violation and packet-level latency performance in large-scale data centers. We establish that stringent flow stickiness carries a significant performance penalty in terms of packet-level delay. Moreover, relaxing the stickiness requirement by a minuscule amount is highly effective in clipping the tail of the latency distribution. We further propose a bin-based load balancing scheme that achieves a good balance among scalability, stickiness violation and packet-level delay performance. Extensive simulation experiments corroborate the analytical results and validate the effectiveness of the bin-based load balancing scheme

Routing and Staffing when Servers are Strategic

Traditionally, research focusing on the design of routing and staffing policies for service systems has modeled servers as having fixed (possibly heterogeneous) service rates. However, service systems are generally staffed by people. Furthermore, people respond to workload incentives; that is, how hard a person works can depend both on how much work there is, and how the work is divided between the people responsible for it. In a service system, the routing and staffing policies control such workload incentives; and so the rate servers work will be impacted by the system's routing and staffing policies. This observation has consequences when modeling service system performance, and our objective is to investigate those consequences. We do this in the context of the M/M/N queue, which is the canonical model for large service systems. First, we present a model for "strategic" servers that choose their service rate in order to maximize a trade-off between an "effort cost", which captures the idea that servers exert more effort when working at a faster rate, and a "value of idleness", which assumes that servers value having idle time. Next, we characterize the symmetric Nash equilibrium service rate under any routing policy that routes based on the server idle time. We find that the system must operate in a quality-driven regime, in which servers have idle time, in order for an equilibrium to exist, which implies that the staffing must have a first-order term that strictly exceeds that of the common square-root staffing policy. Then, within the class of policies that admit an equilibrium, we (asymptotically) solve the problem of minimizing the total cost, when there are linear staffing costs and linear waiting costs. Finally, we end by exploring the question of whether routing policies that are based on the service rate, instead of the server idle time, can improve system performance.Comment: First submitted for journal publication in 2014; accepted for publication in Operations Research in 2016. Presented in select conferences throughout 201

Architecture for Mobile Heterogeneous Multi Domain Networks

Multi domain networks can be used in several scenarios including military, enterprize networks, emergency networks and many other cases. In such networks, each domain might be under its own administration. Therefore, the cooperation among domains is conditioned by individual domain policies regarding sharing information, such as network topology, connectivity, mobility, security, various service availability and so on. We propose a new architecture for Heterogeneous Multi Domain (HMD) networks, in which one the operations are subject to specific domain policies. We propose a hierarchical architecture, with an infrastructure of gateways at highest-control level that enables policy based interconnection, mobility and other services among domains. Gateways are responsible for translation among different communication protocols, including routing, signalling, and security. Besides the architecture, we discuss in more details the mobility and adaptive capacity of services in HMD. We discuss the HMD scalability and other advantages compared to existing architectural and mobility solutions. Furthermore, we analyze the dynamic availability at the control level of the hierarchy

Global attraction of ODE-based mean field models with hyperexponential job sizes

Mean field modeling is a popular approach to assess the performance of large scale computer systems. The evolution of many mean field models is characterized by a set of ordinary differential equations that have a unique fixed point. In order to prove that this unique fixed point corresponds to the limit of the stationary measures of the finite systems, the unique fixed point must be a global attractor. While global attraction was established for various systems in case of exponential job sizes, it is often unclear whether these proof techniques can be generalized to non-exponential job sizes. In this paper we show how simple monotonicity arguments can be used to prove global attraction for a broad class of ordinary differential equations that capture the evolution of mean field models with hyperexponential job sizes. This class includes both existing as well as previously unstudied load balancing schemes and can be used for systems with either finite or infinite buffers. The main novelty of the approach exists in using a Coxian representation for the hyperexponential job sizes and a partial order that is stronger than the componentwise partial order used in the exponential case.Comment: This paper was accepted at ACM Sigmetrics 201