The authors formulate and solve a problem of allocating resources among competing services differentiated by user traffic characteristics and maximum end-to-end delay. The solution leads to an alternative approach to service provisioning in an ATM network, in which the network offers directly for rent its bandwidth and buffers and users purchase freely resources to meet their desired quality. Users make their decisions based on their own traffic parameters and delay requirements and the network sets prices for those resources. The procedure is iterative in that the network periodically adjusts prices based on monitored user demand, and is decentralized in that only local information is needed for individual users to determine resource requests. The authors derive the network's adjustment scheme and the users' decision rule and establish their optimality. Since the approach does not require the network to know user traffic and delay parameters, it does not require traffic policing on the part of the network

Low, Steven L.

Varaiya, Pravin P.

English

Abstruct- We formulate and solve a problem of allocating resources among competing services differentiated by user traffic characteristics and maximum end-to-end delay. The solution leads to an alternative approach to service provisioning in an ATM network, in which the network offers directly for rent its bandwidth and buffers and users purchase freely resources to meet their desired quality. Users make their decisions based on their own traffic parameters and delay requirements and the network sets prices for those resources. The procedure is iterative in that the network periodically adjusts prices based on monitored user demand, and is decentralized in that only local information is needed for individual users to determine resource requests. We derive network’s adjustment scheme and users’ decision rule and establish their optimality. Since our approach does not require the network to know user traffic and delay parameters, it does not require traffic policing on the part of the network. I

Steven H. Low

Pravin P. Varaiya

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A new approach to service provisioning in ATM networks

Caltech Authors - Main

312 IEEfYACM TRANSACTtONS ON NETWORKING. VOL. 2, NO 3, JUNE 1994
Corrections
Correction to “A New Approach to
Service Provisioning in ATM Networks”
Steven H. Low, Member, IEEE, and Pravin P. Varaiya, Fellow, IEEE
We make three corrections to the above noted paper. 1
First, A unit of type s service should simply be a type s connection,
as opposed to ‘a type s connection per unit time’ defined at the
beginning of Section II (Equation (6) is incorrect under the old
definition). It is sold at w, per unit time. Three changes are needed
as a result: i) l/Ts should be edited out from every place it appears;
ii) equation (18) should be multiplied by T., so is the rent in 3) of
User Algorithm; iii) QI and 131are prices per unit of bandwidth and
buffer, respectively, per unit time. Note that the amounts of service
are approximated by continuous variables in the paper.
Second, the welfare function M“ (u’, .r, p ) should be defined as
Fix p With the definition in the paper, an equilibrium (w, .r ) does not
generally maximize W’ subject to conditions (6)--(7). Wkh the new
definition, the unique equilibrium maximizes ~:’ subjeet to conditions
(6)-(7), and the maximum welfare is indeed given by (13) in the
paper, as proved next.
Manuscript received July 21, 1992; revised July 27, 1993; approved by the
IEEJYACMTRANSACTIONSON NETWORKING Editor D. Mitra,
S. H. Low is with the Computing Systems Research Laboratory, AT&T Bell
Laboratories, Murray Hill, NJ 07974 USA. (email: slow@rcsearch.att.tom)
P. P. Varaiya is with the Department of Electrical Engineering and Com-
puter Sciences, University of California, Berkeley, CA 94720 USA. (email:
varaiya@eecs.berkeley .edu)
IEEE Log Number 9403688.
1S. H. ~W ad p. p. Varaiya, lEEHACM Trans. Networking, vol. 1, pp.
547-553, Oct.1993.
Let
{
D; L(.r, )
p. (.rs.u’.,) =
if r,, ~ D.( u. )
u,. if .r, > D,( u,.)
Then the welfare function becomes
W’(w,.r, p) := ~{.r.p. (rs, U’.,) + Vsr.rp[-p,(. r’.!. u’s)])
On the set {(.r. u)[.r. < D~(ILI,)}, ps(.rs,u,) =, D,; l(.r,, ), Hence
aw’
a., =
D;](.r. ) > 0 for .r. < v, and ~ = O, i.e., any
maximizer (.r, w ) must satisfy .rS = D. (u, ) provided condition
(7) is satisfied. We can restrict our search for a maximizer to the set
{(I. U’)!~. = D.( u’,)} and consider the equivalent problem:
maxz >0 v’(.r):= ~.r. (D.; ’(r$)+l)
subject–to equation (7) in paper
By the Kuhn-Tucker theorem, .r” is a maximizer only if 30 ~ O, ,J ~
O such that -
- ~l(nipr~ + ~Ib~(p~,)) ~ O with equality if
.r~ > 0. Since .r~ = DS(U,J) > 0 and - = ll;’(.~), a
necessary condition for (r*. w“ ) to be a maxim~zer is
w; =
~;’(.rl) = X(o,p,. + J,b.$(p,.q))
1
Since l“ is strictly concave ( c)’~~~x) = –diag( + ) < 0), the con-
dition is also sufficient. The assertions now follow from Proposition
1.
Fhally, the second “-” sign in the definition of G(p. n. j) and in
3) of Network Algorithm should be a “+” sign. In Proposition 1, the
complementary slackness condition on (n(p), j( /f ) ) is inadvertently
left out.
ACKNOWLEOOMENT
We thank R. Baldick and G. de Veciana for bringing some of the
errors to our attention.
0 1994 IEEE


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A new approach to service provisioning in ATM networks

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