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We explore settings where it is necessary (due to physical or operational constraints) or desirable (due to synergies or ease of implementation) to assign resources to tasks in a synchronous manner. We model the system as a queueing network with flexible servers and introduce the notion of a configuration to address the synchronous assignment of servers. This allows for a unified approach to determine the effects of resource synchronization, covering a wide range of problems in the literature. The maximal capacity of the system is given by the solution of a linear programming problem that also provides the optimal fractions of time the servers should spend in different configurations. This is used as a basis for constructing policies that have capacity arbitrarily close to the maximal capacity. We contrast synchronous server assignment with an asynchronous approach (focusing on independently scheduling individual servers rather than configurations) and show that synchronous server assignment is attractive with respect to applicability (it can capture constraints on server assignment and synergies among servers), implementation (it may have significantly fewer combinations of server allocations), and capacity (when both are applicable, asynchronous and synchronous server assignment will yield the same maximal capacity). Finally, we illustrate our modeling framework using several examples. [ABSTRACT FROM AUTHOR]

Standard server assignment policies for multi-server queueing stations include the noncollaborative policy, where the servers work in parallel on different jobs; and the fully collaborative policy, where the servers work together on the same job. However, if each job can be decomposed into subtasks with no precedence relationships, then we consider a form of server coordination named task assignment where the servers work in parallel on different subtasks of the same job. We identify the task assignment policy that maximizes the long-run average throughput of a queueing station with finite internal buffers when blocked servers can be idled or reassigned to either replace or collaborate with other servers on unblocked subtasks. We then compare the server coordination policies and show that the task assignment is best when the servers are highly specialized; otherwise, the fully collaborative or noncollaborative policies are preferable depending on whether the synergy level among the servers is high or not. We also provide numerical results that quantify our previous comparison. Finally, we address buffer allocation in longer lines where there are precedence relationships between some of the tasks, and present numerical results that suggest our comparisons for one queueing station generalize to longer lines. [ABSTRACT FROM AUTHOR]

10.1007/s11134-008-9078-5 13 Dai JG, He S. Many-server queues with customer abandonment: Numerical analysis of their diffusion model. Queueing systems with customer abandonments drew a lot of attention in the literature (see [[1], [8]], and [[9]] for earlier exact analysis). We assume that each server can work on only one job at a time and that if both servers are assigned to the same station, they can work together on one job. [Extracted from the article]

We focus on tandem queues with subexponential service time distributions. We assume that number of customers in front of the first station is infinite and there is infinite room for finished customers after the last station but the size of the buffer between two consecutive stations is finite. Using (max, +) linear recursions, we investigate the tail asymptotics of transient response times and waiting times under both communication blocking and manufacturing blocking schemes. We also discuss under which conditions these results can be generalized to the tail asymptotics of stationary response times and waiting times. [ABSTRACT FROM AUTHOR]

The article discusses the optimal static prices for a finite capacity queueing system that serves customers from various classes. It presents that the multi-class formulation can be reformulated as a single dimensional problem wherein the total load is the decision variable. This alternative formulation prove that the upper bound for optimal arrival rates for queueing systems and offer conditions that ensure a unique optimal arrival rate vector.

We study a service facility modeled as a queueing system with finite or infinite capacity. Arriving customers enter if there is room in the facility and if they are willing to pay the price posted by the service provider. Customers belong to one of a finite number of classes that have different willingnesses-to-pay. Moreover, there is a penalty for congestion in the facility in the form of state-dependent holding costs. The service provider may advertise class-specific prices that may fluctuate over time. We show the existence of a unique optimal stationary pricing policy in a continuous and unbounded action space that maximizes the long-run average profit per unit time. We determine an expression for this policy under certain conditions. We also analyze the structure and the properties of this policy. [ABSTRACT FROM AUTHOR]

For a general class of closed feed-forward fork and join queueing networks, we derive the tail asymptotics of transient cycle times and waiting times under the assumption that the service time distribution of at least one station is subexponential. We also argue that under certain conditions, the asymptotic tail distributions remain the same for stationary cycle times and waiting times. [ABSTRACT FROM AUTHOR]

In a G/GI/c loss system with balking, reneging, or limited waiting space, deleting some of the arriving customers can either increase or decrease the fraction of the remaining arrivals who get served, depending on how customers are deleted. We present a model in which the random deletion of arrivals independently and with some fixed probability can never decrease the fraction of the remaining arrivals who get served. [ABSTRACT FROM AUTHOR]

For a Markovian queueing network with two stations in tandem, finite intermediate buffer, and M flexible servers, we study how the servers should be assigned dynamically to stations to obtain optimal long-run average throughput. We assume that each server can work on only one job at a time, that several servers can work together on a single job, and that the travel times between stations are negligible. Under these assumptions, we completely characterize the optimal policy for systems with three servers. We also provide a conjecture for the structure of the optimal policy for systems with four or more servers that is supported by extensive numerical evidence. Finally, we develop heuristic server-assignment policies for systems with three or more servers that are easy to implement, robust with respect to the server capabilities, and generally appear to yield near-optimal long-run average throughput. [ABSTRACT FROM AUTHOR]

Presents a study that examined a finite-capacity queueing system to analyze nonstationary admission control problems in which the system capacity, and the arrival and service rates, may change over time. Background on bias optimal admission control policies; Conditions for a bias optimal policy to be monotonic in time; Results and discussion.

For a system of finite queues, we study how servers should be assigned dynamically to stations in order to obtain optimal (or near-optimal) long-run average throughput. We assume that travel times between different service facilities are negligible, that each server can work on only one job at a time, and that several servers can work together on one job. We show that when the service rates depend only on either the server or the station (and not both), then all nonidling server assignment policies are optimal. Moreover, for a Markovian system with two stations in tandem and two servers, we show that the optimal policy assigns one server to each station unless that station is blocked or starved (in which case the server helps at the other station), and we specify the criterion used for assigning servers to stations. Finally, we propose a simple server assignment policy for tandem systems in which the number of stations equals the number of servers, and we present numerical results that show that our policy appears to yield near-optimal throughput under general conditions. [ABSTRACT FROM AUTHOR]