Server Allocation Policies Research Articles

Optimal Control of Parallel Queues for Managing Volunteer Convergence

Volunteer convergence refers to the influx of volunteers to affected areas after large‐scale disasters. There are not only many benefits to volunteer convergence, but it also creates significant logistical challenges that can impede relief efforts. This study examines polices for admitting volunteers into organized relief operations, and for assigning admitted volunteers to relief tasks. We represent this problem as a queueing system where, in addition to customer arrivals and departures, random server arrivals and abandonments are also present. Then, using a Markov decision process framework, we analyze server admission and assignment policies that seek to minimize relief tasks holding costs as well as volunteer holding and rejection costs. We show that the classic c μ rule, a server allocation policy that determines where to put servers based on relief tasks holding costs and processing requirements, is optimal under both collaborative and non‐collaborative service regimes and when batch server arrivals are allowed. Additionally, we find that the optimal server admission policy is a complex state‐dependent policy. As a result, we propose a class of admission heuristics that depend on the number of workers in the system and the remaining system workload. In a numerical study, we show that our heuristic policies perform well with respect to long‐run average costs, waiting times, number of volunteers in the system, and number of volunteers idling in the system over a range of parameter values and distributions that are based on real data from a case study. As such, they promise volunteer coordinators an effective and simple way to manage disaster volunteers.

Bayesian modeling of abandonments in ticket queues

AbstractTicket queues (TQs) issue tickets to customers upon arrival, and are often used in the public and private sectors. Abandonment data collected by TQs is interval censored, which makes predicting customer abandonments a challenging problem. In this paper, we build a Bayesian framework for predicting abandonment counts in TQs to assist managers in workforce planning. In doing so, we propose parametric and semiparametric modulated Poisson process models and develop their Bayesian analyses using Markov chain Monte Carlo methods. We implement our models using actual abandonment data from a bank's TQ, and illustrate how we can provide managerial insights related to abandonment counts and server allocation policies.

Bayesian Modeling of Abandonments in Ticket Queues

Ticket queues arise often in public and private sector operations. The service providers in ticket queues have limited information on customer abandonments because abandonment time data is interval censored. The censored nature of data poses challenges in modeling and analysis of abandonments and in developing staffing policies. To alleviate such challenges, we present a Bayesian framework for analysis of abandonments in ticket queues. In doing so, we propose parametric and semi-parametric modulated Poisson process models to describe the abandonment behavior and develop their Bayesian analysis using Markov chain Monte Carlo methods. We implement our models on actual abandonment data from a bank’ s ticket queue and illustrate how the proposed Bayesian framework can be used to provide insights for operations managers in predicting abandonments and in developing server allocation policies.

On the Stability Region of Maximum Weighted Matching Server Allocation Policy

In this paper, we study the stability region of a multi-server queueing system for which Maximum Weighted Matching (MWM) server allocation policy is known to be throughput-optimal. We derive a linear algebraic characterization of the system stability region polytope (or equivalently MWM stability region) by means of a finite set of linear inequalities. Such a characterization of the stability region is useful for solving network stochastic optimization problems and also evaluating the performance of MWM server allocation policy, e.g., deriving explicit performance bounds for the average queueing delay and flow measurement metrics. Furthermore, using the linear algebraic form of the stability region, we derive an upper bound for the average queueing delay of MWM policy.

Flexible Server Allocation and Customer Routing Policies for Two Parallel Queues When Service Rates Are Not Additive

We consider the question of how routing and allocation can be coordinated to meet the challenge of demand variability in a parallel queueing system serving two types of customers. A decision maker decides whether to keep customers at the station at which they arrived or to reroute them to the other station. At the same time, the decision maker has two servers and must decide where to allocate their effort. We analyze this joint decision-making scenario with both routing and station-dependent holding costs, but add an important twist. We allow the combined service rate (when the servers work at the same station) to be superadditive or subadditive. This captures positive or negative externalities that arise during collaboration. We seek an optimal control policy under the discounted or long-run average cost criteria. Our results show that in the superadditive case jobs should never be routed away from the lower-cost queue. When jobs are rerouted from the higher-cost queue to the low-cost queue the optimal control is monotone in the respective queue lengths. Moreover, we show that the optimal allocation is a nonidling priority rule based on the holding costs. In the subadditive case we find that the optimal policy need not exhibit such a simple structure. In fact, the optimal allocation need not prioritize one station (it may split the servers), and the optimal routing need not be monotone in the number of customers in each queue. We characterize the optimal policy for a few canonical cases and discuss why intuitive policies need not be optimal in the general case. An extensive numerical study examines the benefit of dynamically controlling both routing and resource allocation; we discuss when using one of the two levers—dynamic routing and dynamic allocation—is sufficient and when using both controls is warranted.

In This Issue

In This Issue

Performance analysis of mobile communication networks

Models and analytical techniques are developed to evaluate the performance of wireless or mobile communication networks that can be represented by a single buffer multiple queues system. Specifically, we developed a non-linear model of uncertainty for analysing a polling system with periodic nondeterministic server allocation policy, Bernoulli feedback of customers, server timeouts, randomly time varying connectivity, correlated input processes, and single buffers. Our model encompasses a variety of examples. The periodic nondeterministic server allocation is a new class of server allocation to queues policy. Some well-known special cases of this policy are cyclic, periodic and random polling. We were able to perform both transient and steady state analysis. The steady state analysis allows us to compute several performance measures including the expected response time, loss probability, throughput and mean cycle time. Performance measures obtained from our analysis provide us with some guidelines for regulating flows through the system.

A note on preemptive scheduling of multiclass jobs with geometric service times and hard deadlines

We consider the scheduling of multiclass jobs with deadlines to the completion of their service. Deadlines are deterministic and job arrivals in each class occur at the times of deadline expirations in the respective class. Assuming geometric service times with class dependent means, we derive structural properties of preemptive server allocation policies that maximize the expected number of job completions. Our work extends results that have appeared in the real-time wireless scheduling literature.

On the Role of Queue Length Information in Network Control

We study the role played by queue length information in the operation of flow control and server allocation policies. We first consider a simple model of a single server queue with congestion-based flow control. The input rate at any instant is decided by a flow control policy, based on the queue occupancy. We identify a simple “two-threshold” control policy, which achieves the best possible exponential scaling for the queue congestion probability, for any rate of control. We show that when the control channel is reliable, the control rate needed to ensure the optimal decay exponent for the congestion probability can be made arbitrarily small. However, if control channel erasures occur probabilistically, we show the existence of a critical erasure probability threshold beyond which the congestion probability undergoes a drastic increase due to the frequent loss of control packets. We also determine the optimal amount of error protection to apply to the control signals by using a simple bandwidth sharing model. Finally, we show that the queue length based server allocation problem can also be treated using this framework and that the results obtained for the flow control setting can also be applied to the server allocation case.

Evaluating the optimal server allocation policy for clusters with on/off sources

We investigate a system with reconfigurable servers and bursty arrival streams for different job types. The problem of when to reallocate servers from one job type to another will then be formulated as a Markov decision process. We will show that solving this Markov decision process is very problematic for any but the most simple systems, demonstrating the need for heuristics. The performance of several heuristic allocations will be compared to that of the optimal policy for some cases and shown to yield reasonable performance.

Static and dynamic server allocation in systems with on/off sources

A system consisting of a number of servers, where demands of different types arrive in bursts (modelled by interrupted Poisson processes), is examined in the steady state. The problem is to decide how many servers to allocate to each job type, so as to minimize a cost function expressed in terms of average queue sizes. First, an exact analysis is provided for an isolated IPP/M/n queue. The results are used to compute the optimal static server allocation policy. The latter is then compared to four heuristic policies which employ dynamic switching of servers from one queue to another (such switches take time and hence incur costs).

Optimal stochastic scheduling of two interconnected queues with varying service rates

We consider two-stage tandem queueing systems attended by two specialized and one flexible server, where all servers have time varying rates. Assuming exponential processing times and linear holding costs, we derive properties of server allocation policies that minimize expected costs over an infinite time horizon.

Dynamic Scheduling of a Multiclass Fluid Model with Transient Overload

We study the optimal dynamic scheduling of different requests of service in a multiclass stochastic fluid model that is motivated by recent and emerging computing paradigms for Internet services and applications. In particular, our focus is on environments with specific performance guarantees for each class under a profit model in which revenues are gained when performance guarantees are satisfied and penalties are incurred otherwise. Within the context of the corresponding fluid model, we investigate the dynamic scheduling of different classes of service under conditions where the workload of certain classes may be overloaded for a transient period of time. Specifically, we consider the case with two fluid classes and a single server whose capacity can be shared arbitrarily among the two classes. We assume that the class 1 arrival rate varies with time and the class 1 fluid can more efficiently reduce the holding cost. Under these assumptions, we characterize the optimal server allocation policy that minimizes the holding cost in the fluid model when the arrival rate function for class 1 is known. Using the insights gained from this deterministic case, we study the stochastic fluid system when the arrival rate function for class 1 is random and develop various policies that are optimal or near optimal under various conditions. In particular, we consider two different types of heavy traffic regimes and prove that our proposed policies are strongly asymptotically optimal. Numerical examples are also provided to demonstrate further that these policies yield good results in terms of minimizing the expected holding cost.

Stochastic Approximations and Adaptive Control of a Discrete-Time Single-Server Network with Random Routing

This paper considers a discrete-time system composed of K infinite capacity queues that compete for the use of a single server. Customers arrive in independent and identically distributed (i.i.d.) batches and are served according to a server allocation policy. Upon completing service, customers either leave the system or are routed instantaneously to another queue according to some random mechanism. As an alternative to simply randomized strategies, a policy based on a stochastic approximation algorithm is proposed to drive a long-run average cost to a given value. The underlying motivation can be traced back to implementation issues associated with constrained optimal strategies.A version of the ordinary differential equation (ODE) method as given by Metivier and Priouret is developed for proving almost sure convergence of this algorithm. This is done by exploiting the recurrence structure of the system under nonidling policies. A probabilistic representation of solutions to an associated Poisson equatio...

Scheduling service in tandem queues attended by a single server

Consider a tandem queue model with a single server who can switch instantaneously from one queue to another. Customers arrive according to a Poisson process with rate λ . The amount of service required by each customer at the ith queue is an exponentially distributed random variable with rate μi. Whenever two or more customers are in the system, the decision as to which customer should be served first depends on the optimzation criterion. In this system all server allocation policies in the finite set of work conserving deterministic policies have the same expected first passage times (makespan) to empty the system of customers from any initial state. However, a unique policy maximizes the first passage probability of empty-ing the system before the number of customers exceeds K, for any value of K, and it stochastically minimizes (he number of customers in the system at any time t > 0 . This policy always assigns the server to the non empty queue closest to the exit

Bandwidth Allocation Strategies in Wide-Band Integrated Networks

A common digital transmission facility in a wide-band integrated service digital network (ISDN) provides shared access to a community of heterogeneous users. Traffic demands from these users vary in their arrival rate, their service time, and their bit rate. In order for this type of communication system to handle its traffic demands with high efficiency and flexibility, a close control of access to the shared bandwidth is required. We model the system by a general multiserver queueing system where customers demand service from a random number of servers. If no waiting is allowed, this queueing model is readily analyzed, and various server allocation strategies can be studied. If the various access requests are queued for service, then the system calls for efficient strategies for allocating servers to waiting customers. In this case, exact analysis of the underlying queueing model becomes quite difficult. For this case, we present some analytic and simulation results of the performance of the system under several server allocation policies.