Stochastic Processing Networks Research Articles

Delay performance in stochastic processing networks with priority service

We evaluate the delay performance of an open multi-class stochastic processing network of multi-server resources with preemptive-resume priority service. We show that the stationary distribution of aggregate queue lengths has product form. For each service class we derive explicit expressions for the following stationary performance measures: The mean and, under feedforward routing, the Laplace transform of the delay distribution at each resource. We show that these measures are the same as if the resources were operating in isolation.

Two Workload Properties for Brownian Networks

As one approach to dynamic scheduling problems for open stochastic processing networks, J.M. Harrison has proposed the use of formal heavy traffic approximations known as Brownian networks. A key step in this approach is a reduction in dimension of a Brownian network, due to Harrison and Van Mieghem [21], in which the “queue length” process is replaced by a “workload” process. In this paper, we establish two properties of these workload processes. Firstly, we derive a formula for the dimension of such processes. For a given Brownian network, this dimension is unique. However, there are infinitely many possible choices for the workload process. Harrison [16] has proposed a “canonical” choice, which reduces the possibilities to a finite number. Our second result provides sufficient conditions for this canonical choice to be valid and for it to yield a non-negative workload process. The assumptions and proofs for our results involve only first-order model parameters.

Continuous-Review Tracking Policies for Dynamic Control of Stochastic Networks

This paper is concerned with dynamic control of stochastic processing networks. Specifically, it follows the so called “heavy traffic approach,” where a Brownian approximating model is formulated, an associated Brownian optimal control problem is solved, the solution of which is then used to define an implementable policy for the original system. A major challenge is the step of policy translation from the Brownian to the discrete network. This paper addresses this problem by defining a general and easily implementable family of continuous-review tracking policies. Each such policy has the following structure: at each point in time t, the controller observes the current vector of queue lengths q and chooses (i) a target position z(q) of where the system should be at some point in the near future, say at time t+l, and (ii) an allocation vector v(q) that describes how to split the server's processing capacity amongst job classes in order to steer the state from q to z(q). Implementation of such policies involves the enforcement of small safety stocks. In the context of the “heavy traffic” approach, the solution of the approximating Brownian control problem is used in selecting the target state z(q). The proposed tracking policy is shown to be asymptotically optimal in the heavy traffic limiting regime, where the Brownian model approximation becomes valid, for multiclass queueing networks that admit orthant Brownian optimal controls; this is a form of pathwise, or greedy, optimality. Several extensions are discussed.

From Project to Process Management: An Empirically-Based Framework for Analyzing Product Development Time

While product development efforts are often viewed a unique configurations of idiosyncratic tasks, in reality different projects within an organization often exhibit substantial similarity in the flow of their constituent activities. Moreover, while most of the planning tools available to managers assume that projects are independent clusters of activities, in reality many organizations must manage concurrent projects that place competing demands on shared human and technical resources. This study develops an empirically-based framework for analyzing development time in such contexts. We model the product development organization as a stochastic processing network in which engineering resources are “workstations” and projects are “jobs” that flow between the workstations. At any given time, a job is either receiving service or queueing for access to a resource. Our model’s spreadsheets quantify this division of time, and our simulation experiments investigate the determinants of development cycle time. This class of models provides a useful managerial framework for studying product development because it enables formal performance analysis, and it points to data that should be collected by organizations seeking to improve development cycle times. Such models also provide a conceptual framework for characterizing commonalities and differences between engineering and manufacturing operations.