Take Action

Home | Faculty & Research Overview | Research

Research Details

Brownian Models of Closed Queueing Networks: Explicit Solutions for Balanced Three-Station Systems, Annals of Applied Probability


We study a closed, three-station queueing network with general service time distributions and balanced workloads (that is, each station has the same relative traffic intensity). If the customer population is large, then the queue length process of such a network can be approximated by driftless reflected Brownian motion (RBM) in a simplex. Building on earlier work by Harrison, Landau ands Shepp, we develop explicit formulas for various quantities associated with the stationary distribution of RBM in a general triangle and use them to derive approximate performance measures for the closed queueing network. In particular, we develop approximations for the throughput rate and for moments and tail fractiles of the throughput time distribution. Also, crude bounds on the throughput rate and mean throughput time are proposed. Finally, we present three examples that test the accuracy of both the Brownian approximation and our performance estimates.




Elizabeth Schwerer, Jan A. Van Mieghem

Date Published



Schwerer, Elizabeth, and Jan A. Van Mieghem. 1994. Brownian Models of Closed Queueing Networks: Explicit Solutions for Balanced Three-Station Systems. Annals of Applied Probability. 4(2): 448-477.


Explore leading research and ideas

Find articles, podcast episodes, and videos that spark ideas in lifelong learners, and inspire those looking to advance in their careers.
learn more


Review Courses & Schedules

Access information about specific courses and their schedules by viewing the interactive course scheduler tool.


Discover the path to your goals

Whether you choose our Full-Time, Part-Time or Executive MBA program, you’ll enjoy the same unparalleled education, exceptional faculty and distinctive culture.
learn more

Take Action