1026 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 58, NO. 4, APRIL 2010
A Recursive Algorithm for Bandwidth Partitioning
Scott Jordan, Member, IEEE, Sam Charrington, and Pruttipong Apivatanagul
Abstract—We consider complete partitioning of bandwidth
among multiple services. When class bandwidth is an integer
multiple of the next lower class and total bandwidth is an
integer multiple of the largest class bandwidth, we develop
a recursive algorithm that determines the optimal complete
partitioning policy with a significantly lower complexity than that
of known dynamic programming or mixed integer programming
approaches.
Index Terms—Resource management, access control.
I. INT RODUCTION
T
HE problem of allocation of a network resource to
multiple services arises in many areas o f networking.
Often, m ultiple services share a single resource. Allocation
of this resource is generally determined by a combination
of connection access control and packet scheduling policies.
Although cross-layer approaches may achieve superior results,
in connection-oriented packet-switched networks connection
access control and packet scheduling are often segmented by
analyzing them on different time scales in order to maintain
modularity, see e.g. [1], [2]. In this segmented approach,
packet scheduling is considered on the packet time scale,
and each connection’s resource demands are described by
averaging across the connection duration. Connection access
control uses these averaged resource requirements to allocate a
shared resource am ong multiple service classes. Multiplexing
gains are thus modeled separately on packet and connection
time scales, and packet level QoS and connection level QoS
are treated separately.
Such a segmentation reduces the connection access control
problem to a classical problem of the sharing of bandwidth
on a single link in a circuit-switched network that supports
multiple service classes defined by the bandwidth required per
connection, see e.g. [1]. This classical problem also appears
in a wavelength division multiplexed network, see e.g. [3 ].
The two simplest admission control policies are complete
sharing (in which all connections share the entire link band-
width and a connection is admitted if there is sufficient
free bandwid th on the link) and complete partitioning (in
which the link band width is partitioned among classes and
a connection is admitted if there is sufficient free bandwidth
Paper approved by T. T. Lee, the Editor for Switching Architecture Perfor-
mance of the IEEE Communications Society. Manuscript received March 13,
2009; revised August 18, 2009.
S. Jordan is with the Department of Computer Science, Uni versity of
California, Irvine, CA 92697 (e-mail: sjordan@uci.edu).
S. Charrington contributed to this project while he was with the Department
of Electrical Engineering and Computer Science, Northwestern University,
Evanston, IL 60208.
P. Apivatanagul contributed to this project while he was with the Institute
of Transportation Studies, University of Calfornia, Irvine, CA 92697.
Additional work on this project was provided by Jie Hu.
Digital Object Identifier 10.1109/TCOMM.2010.04.090041
in that class’s allocation). Intermediate policies include trunk
reservation (in which a reservation parameter is set for each
class a nd a connection is admitted if the fre e bandwidth on
the link exceeds the reservation parameter) and coordinate
convex policies (in which a connection is admitted if the
resulting vector of the number of active connections in each
class remains within a specified convex subset of the state
space), see e.g. [4]. Although trunk reservation and coordinate
convex po licies can usually outpe rform complete sharing and
complete partitioning policies, complete partitioning is often
used for simplicity. Complete p artitioning policies contin ue
to arise in many areas in networking, see e.g. [5] for use in
virtual private networks (VPNs), [6], [7] for use in Multiple
Packet Label Switching (MPLS) and/or Integrated Services
(IntServ), [8]–[10] for use in wireless networks, and [11] for
use in application composition.
In this paper, we consider connection access control policies
that use complete partitioning of a single resource, here
considered to b e bandwidth. We presume that th e system
attempts to either maximize the revenue gen erated by admitted
connections or to minimize a weighted sum of blocking
probabilities. Although these optimization metrics are the most
commonly considered in this problem, we note that other met-
rics and constraints are sometimes considered, see e.g. [12].
In addition, often connection access control policies consider
allocation of multiple resou rces, see e.g. [1], [4]. Complete
partitioning can be used as a static resource allocation strategy,
in which case the computational complexity may not be an
issue. However, complete partitioning is often considered as
a dynamic resource allocation strategy, by recomputing the
optimal complete partition whenever the traffic load changes
significantly [12]. In this case, the time required to compute
the optimal policy can be critical. A dynamic programming
approach to the determina tion of the optimal solution was
provided in [13], and a mixed integer programming approach
was provided in [14]. Let 𝐾 denote the number of classes
and 𝑚 denote the number of resources. The complexity of the
dynamic p rogramming approach is 𝑂(𝐾𝑚
2
). The complexity
of the mixed integer programming approach has not been
analytically determined; n umerical evaluations show that it is
lower than that of the dynamic programming approach, but
that it can still be unacceptably high for systems with a large
number of shared resources.
We consider complete partitioning in the case in which
the resource demand of a class is an integer multiple of
the demand of the next lower class. This integer relationship
holds in most systems in which complete partitionin g is
used. In addition, we assume that the total bandwidth is
an integer multiple of the largest class bandwidth. Under
these assumptions, we develop a recursive algorithm that
determines the optimal complete partitioning policy with a
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