A scheme for handling connectionless services in connection-oriented networks

(1)

A.n Approach t o Manage Connectionless Services in

Connect ion- Qriented Networks*

Muhammet

ARDELATI

and

Erdal

ARIKAN

Phone (90) 312-2664862 Fax (90) 312-2664126 E-mail: muliammet@ee.bilkent.edu.tr Electrical and Electronics Engineering Department, Bilkeiit University 06533, Ankara, Turkey

Abstract- I n t h i s work we propose a pricing schcine which servcs as a n i n s t r u m e n t for iiianagiiig con- iiectioiilcss services i n coiiiiection-oriented coiiiinu- iiicatioii networks. T h e schcine is able t o allocat,a network b a n d w i d t h i n a Pareto-optiiiial way that iiiaxiniizes t h e t,otal surplus. The key idea is to decompose t h e scrvico provision proccdure aiiioiig t h r e e s e p a r a t e parties whose interactions are gov- eriicd b y a set of' coiupctitive pricing mecliaiiisms.

I. IHTRODUCTIOK

Conlieclion-oriented net,works are well-suit,ed t o handle interactive ancl real-time applicat,ions such as telephony ancl video conferelicing. However, they will be under- nt,ilized if used directly in applications characterized by sporadic behavior and short service time requirements such as iiiail and file transfer. For such applications, in which t,he user information typically consists of a single block of d a t a , connection-oriented services are inefficient due to connect,ion establishment and tear-

doivii overhead. Such applications are more efficiently

handled by a connectionless service which multiplexes data. froin individual applicat,ions into a pre-established virtual connection.

T h e aim of this paper is t o propose a method for providing coniiectionless services in a connection-oriented iiet-

work. ( A n important instance of this problem, which

iiiotivated t,lie present work, is LAN intserconiiection over an ATM network.) Several solutions have been proposed for t,his problem [1, 2, 31. A general discus-

sion of this problem can he found in [4, 5,

61.

The approach proposed in this paper is based on a pricing scheine which allocates the communication re-

sources in a Pareto-optimal way t h a t achieves maxi-

11111111 t,otal surplus

[TI.

In fact, pricing plays an im- I)ortaiit role in any complet,e network architecture. If services were free, there would be no incentive t o re- quest, less t,han t,hc hest service the network could pro-

\-itle. which would not produce effect.ive utilization of

1 lie i1et.work rcsources. There have been several papers

dealing w i t h pricing as a means of resource allocatioii i n iiitegratcd net,works, see, e.g., [S, 9 , lo]; however, iione risecl it as a. iiiea.ns of providing connectionless traffic slipport, in coiiiiection-orielIled iietworks.

* r 1

I his r'cseai c l 1 was supported b y TURITAK uiider project lEEL.4G.$l:3.

Users Layei

,

Arbiters Layer

Nrtwork Layer

Pig. 1. Fiinctional decomposition

In certain aspects, our work falls between i . 1 1 ~

reservation-orieiited approach in [g, 101 and the best- effort type approach in [8]. Description of the proposed scheme is given in Section 11. Section 111 presents s o m e simulation results and finally in Section IV, coininents and conclusions are given.

11. THE

PROPOSED

SCHEME

In our proposed scheme we introduce a class of agents which we call arbzters to manage the connectionless service. Arbiters are service providers who buy connection-oriented services (bearer services) from the network and sell connectionless services (leleservices) to users. Arbiters operate in a free-competition environ- ment, in certain respects siiniiar to service provisioii by multiIile long-distance phone compaiiies. T h u s we have a functionally inodular framework i n which there are three layers interacting with each other in a hierarchi- cal manner as sketched in Fig. 1 .

A .

The Model

For simplicity of exposition, we consider here a. simple network coiisisting of a single origin-destination pa.ir

( o - d ) connect,ed by a virtual channel of capacity I< channels. Each cliaiiiiel is assumed t,o be a delayless, errorless bit, pipe.

A n

arbiter leases from t h e network

a certain nrirnber of clmiiiels, which we call a 6 7 4 for a fixed "time period t,liat is orders of magnitude longer than the d u n t i o n of a typical connectionless service. Periodically, the network holds auctions to serve tho entry or expansion requests of the arbiters. T h e net-

work charges the arbiters a per-unit-time channel fee of

p ( k ) where I; is t,he total niimher of cliannels hired to

all the arbiters.

0-7803-31 -09-5/96/$5.00

0

1996

IEEE

(2)

Table 1: Tr iflic Specifications.

Exprejs mail

FTP

__

‘rliere arc 4 service classes labeled A , U , C and D. Class

r E { A j B. C , D} is cliaiacterized by a pair (a,, T,) i l l -

clicat,ing that, the servicl: requires a, channels for a dii-

iown in Table 1 . Only class A t,raflic inscasitive to quelling delay.

o service class z arrive at tlic iiet,work = A r ( u z ) wherc I J . ~ is t81ic prcvailiitg p(Tr-iiiiit-tiinc. cliaiiiicl prilx cliarged t,o users of service

iZ user of lype .c IE { U , C , D} arriving, at tiriie 1 Cor ; i n arbitcr wlm has 0,. cli

csist,s, t,Iie user is lost,.

[I

a n arbiter esist.s with a, free

cllaiiiieis, tlie user i s ,Je’J for

T,

seconds and pays tlie

arliitcr t.hc amount p . . Users of type A are never lost;

i.lic!- join t11c cliieue of 1 litis a n d are served wlieiievcr

t h e hiis is idle. The quality of service is measured by

t h e delay for service class A and tlic probability of loss

for classes U ,

C,

and D.

B.

P i i c i n g of

Seraices

TI%

p ~ ) p o s e a pricing scheme based on risk analysis

t.liat, i s well k11ow11 in finance literature [11, 121. Let 41, he an index which rcf1c~:t:i the randomness of revenues of service class 2 : . Tlie specific risk index used here is

ddiiied in tlie next sulisection. The arbiters set t,l-ie price for service x as

iclierc. tlic risk index and tlic fuiic1,ion p arr such that,

/ 1 ( + . ~ 1 ) = 0. \Ve call p(<b,) a risk p ” u m charged t80 class E since t,lic uncertainty in future reveillies i s a type

of risk and a.rbiters ask a premium as cornpensation.

111 frcc coinpetit,ion markets there are inariy arllitela,

’ ill he a t t r x t . e d 1.0 that arbiter which nslis

i, price. T-Teiice the market, puice fnnctioii will

I > c t,iic\ io w c r , c n c:elope of‘ t.hc price functioiis offered by

as illustrabed ii r i g . 2.

tin>. ;irl)ikr. \rho ~ v o u l c lilie to persist in tlic marltr:t

hlioiiltl Iia~.e ;:.t !east a port,ion of its price fuiict,ion t>aw

gciit 1.0 t,he uiarltet, price function. Cornpetition and

L‘ri,c-c:iii ry i n t o market will always force a r b i k r s l o lowcr

i l i r i r i)i.icc fiiiicl,ioiis.

Risk, $

’’ Fig. 2. Price functions.

tial per-uiiit-time revenue r i , j ( t ) given b y

where

E{

.} denotes expectation. Kote that &(f) in-

cludes the pot,ent,ial reveiiue unrealized due t,o uiiiuet demand. The risk index used in this work is

where R,,(t) i:, the inarltet revenue given by

Note t h a t

4.4

== 0 arid

CZe(A,a,c,Dl

4,

= 1

D. Equilibrium Analysis

(4)

There are several approaches to investigate t h e welfare properties of t,he competitive markets. Tlie one we pur- sue here, the discrete good mode[ approach, is probably the simplest. In this approach there are two goods: and z , y are the clinnnels and z is tlie iiioii~y left for purchasing other goods. A user utility function is de- fined its

where p is tlir clianiiel’s price and 7 3 is the user’s biitl-

get. The uscr’:i surplus, s j ~ is defined os the cliarige i11 liis utility after malting a decision. That is

The rcservatioii price is that price pj wilijcli just nixltes

t,lie coiisi~~iic~’ intlilferent to being scrvcd or imt. ‘rltat~

(3)

Asstiiniiig quasilinear preferences [ 7 ] , (8) inay be rewrit- t.cn as

ip price Blocking

($) prob

I Siil,st,itut,ing iii ( 7) ) one c a n easily show t,hat the user’s

sllrplils reduces t,o

Waiting A,

time (min) (user/s)

F

‘Thr aggregate users’ surplus,

S,,

, is the sum o f individ-

U;II surpluses. ’To find t,lie iietivorl; surplus at an out- 1 o f I;‘ cliaiiiiels, iiote that. all ii chaiiiiels are

l i i i . i . i i \ v i t , I i a price of p ( I < ) . Hoi

( k z 1 . .... I<) 1ia.s a n opportiiiiity cost of p ( k ) . Tliere-

few, it coiitri1)utes t o the urt~vorlc surplus the a m o u n t

] J ( i<) ~ ii(.A.). aiitl t h e t o t , n l net\vork surplus is given by

i = 1

T h c x arhitcrs’ siirplus is defincd to be their total profits

gi\wl Iy

111 this sxi,ioii we preseiit, siinulation results for an

iiiple tliat, deiiioiist,rates the basic feat,ures of our

~riinici~orl;. Wc compare our competitive inarltet with

a irioiiopolisi,ic one. The example network consists of

a iiiiglc iiode and si1 oui.l)iit link of capacity 75 M B / s

i ~ l i i c h is equivalent t o 750 clianncls. We assume that it, is cic~sii~ccl i,o allocate not m o r e tlian 2.5% of the link c;il)acit>. i o connectionless t r a f i c . To t,liis end, tlie network iises t,li(> 1)rice function

Table 2: Results for a single-a.rbiter network.

expected value of profits exceeds its st,aiidard devia- t,ioii. T h e arhitkr aims at, masiniiziiig its profit through set.t,ing piices t,o tlie teleservices and adjusting its band- width given thats the profit, exceeds its s t a n d a r d devi- ation. We assumed the risk preiiiium t o be p ( 4 ) =

0.

Three hours of net.nTorlt operatioii was simulated ( a h o u t

two hours CPlJ l i i i i c . on n SlTN ivor1;slatioii) ‘The result-

iiig figures are suiriinarized i n Tables 2 aiid 4 . T h e risk

indexes ivcrc cst,iinated oiice encli 60 sccoiids a s follows:

\~lic.rc r,, is the reveiiiie of service class 3; a t time t .

r,

aut1 I.,,, are the aritbinctic: averages of aiid I’,,,

respcctively and 60 represents t h e nuinlier of samples in our specific exaiiiple.

The revenue, profit, and surplus are expressed a.s per- unit-time values. Illiring a t8iinc: period T , t,he arbit,er’s

rate of reveiiiie is calculatcd as

where for class 3: users,

Mz

and P , ~ represent the iiuin-

ber of served uscrs aiid t,he price charged froin t,hem respectively. If

I<

is the iiuniher of channels leased b y the arbiter, then the fee paid t o the iietworlr is

i < p ( K ) = 30001i/(750-11<). Subtract,ing this fee froin

t,he arhiter‘s revenue, w e h i d the profit wliicii is the nr- biter’s surl)lus. The network’s and users‘ surpluses arc calcula.t,ed as follows:

(4)

TaI,le :i Itcwlts for tlirecl-arbiter iietworli

'rii!>le 4: Coiiiparisoii I)ctareen performance iiieasures.

. $-'or. c~saiiil)ii. t,lic, uiiit, p r i c t of classes C oss t h a i i that o f CIRS:: U . On llie oilier hand, iiltliougli uscrs of classc:;

(I:

aiid D have t,lie sanic size, those of class

il

are cliaigc-d lcss I~ecause class

C

t,rafllc

11 e 17 er for 111 a ii c e iiic ;F 11 res, TVC not e t 11 a.t t2 11 c iii~tworli aiid the uscrs ai'e better OR under coinl)etii,ioii; tlicir suri)luses are incn,a!jerl. illso, prices and hloclc-

in& prohaI>iliLies are significaiit,ly improved. Altliongh

iiioiiol)oly results in a higher degree of utilization, it, rc:-

srilt,s i n a cot~respoiidjiigly higlicr blockiiig prol>abilily.

ase of monopoly w r iiot,e t,lint the equilibriurri in

c i t # y a.ntl prices oc(:ur a t i,he poiiit of iiiaxiiiiuiii prolit ~ wliiie rinder coiiip?t,ition, equilibrium occurs ;it

i lrci point, of niasiniiirii total surplus.

t,liat Ihe profit,:: iiia.dc hy arhii,ers are minimized. This

means (,hat network services will be provided t o elid-

users almost transparently and arbiters a c t o n l y as a

tool of managing aiid dimensioning network resources. 111 this paper we izdtiressed a. siiigle U-rl pair. The riel-

work c i t s ~ is investigatcd in [13].