Power-spectrum-based neural-net connection admission control for multimedia networks

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Power-spectrum-based neural-net connection

admission control for multimedia networks

C.-J. Chang, L.-F. Lin, S.-Y. Lin and R.-G. Cheng

Abstract: Multimedia networks need sophisticated and real-time connection admission control (CAC) not only to guarantee the required quality of service (QoS) for existing calls but also to enhance utilisation of systems. The power spectral density (PSD) of the input process contains correlation and burstiness characteristics of input traffic and possesses the additive property. Neural networks have been widely employed to deal with the traffic control problems in high-speed networks because of their self-learning capability. The authors propose a power-spectrum-based neural-net connection admission control (PNCAC) for multimedia networks. A decision hyperplane is constructed for the CAC using power spectrum parameters of traffic sources of connections, under the constraint of the QoS requirement. Simulation results show that the PNCAC method provides system utilisation and robustness superior to the conventional equivalent capacity CAC scheme and Hiramatsu’s neural network CAC scheme, while meeting the QoS requirement.

1 Introduction

Multimedia networks should be equipped with a set of traffic control functions to ensure the QoS of each service connection and to enhance system utilisation. One of the traffic control fLinctions is connection admission control. Connection admission control (CAC) is defined as ‘a set of actions taken by the network to deter- mine whether a connection can be accepted’ [l]. A new connection is accepted only if sufficient network resources are available and the required performance can be maintained.

Several conventional CAC control techniques for high- speed networks have been proposed. In the peak rate allocation, QoS is always guaranteed if the aggregate bit rate never exceeds the system capacity. However, it leads to low utilisation of network resources. An equivalent capacity (effective bandwidth) method was proposed to estimate the required bandwidth for individual or aggregate connections with desired QoS [2, 31. A call admission scheme by inferring the upper bound of cell loss probability from the traffic parameters specified by users was studied in [4]. Also a simple bandwidth assignment policy by classifying all traffic sources was presented. All the studies were conducted mainly on the basis of traffic parameters in the time domain.

However, Li and Hwang [5] and Sheng and Li [6] have studied the queueing performance of a high-speed network from the point of view of frequency-domain traffic parameters. The process of input traffic inherently contains a power spectral density (PSD) function, which is the Fourier transform of the input traffic process’s autocorrelation function. From their studies, two characteristics of

$3 IEE, 2002

IEE P,amL.clirzg..r online no. 2002003 1 DOT IO. 1049/ip-c01n:2002003 I

Papcr first received 13th November 2000 and in reviscd Tomi 18th September 200 1

The authors are wilh thc Department of Communication Engineering, National Chiao Tung University, Hsinchu 300, Taiwan, Reptiblic of China

PSD are demonstrated: (i) the PSD can be represented by three main parameters such as the DC component, the average power and the half-power bandwidth; and (ii) the low-frequency band of the input PSD has a dominant impact on queueing performance, while the high-frequency band can be neglected to a large extent.

This is because the low-frequency component of the PSD contains the correlation and burstiness of the input process. With more low-frequency components, the burstier the input traffic will be [7].

We have proposed a composition algorithm to obtain three new PSD parameters of a traffic source which is aggregated from two traffic sources in [8]. It can be concluded that PSD parameters possess the additive property; this makes the PSD parameters more suitable for admission control, no matter how many types of traffic sources there are. A power-spectrum-based table-lookup CAC method for multimedia communications in ATM networks was studied, where the table content was the cell loss probability indexed by PSD parameters of voice/video calls and arrival rates of data calls [SI. Simulation results revealed that it could achieve system utilisation 9% higher than that of the conventional equivalent capacity CAC method proposed in [2].

In recent years, neural networks have been widely employed to deal with the traffic control problems in high-speed multimedia networks [9-1 I]. A major feature of the neural network is the self-learning capability which can be utilised to characterise the relationship between input traffic and system performance. In [9], Hiramatsu proposed a connection admission controller using a neural network. Hiramatsu’s neural network connection admission control- ler used the offered traffic characteristics and QoS requirement to decide whether to accept or reject a new call. Results showed that the neural network learned a complicated boundary for call acceptance decision. We previously proposed a neural network connection admission control (NNCAC) scheme [lo] and a neural fuzzy connection admission control (NFCAC) scheme [I 11 for ATM networks. Simulation results reveal that call admission control with either neural networks or neural fuzzy

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networks can improve significantly the system utilisation under QoS constraint.

In this paper, we propose a power-spectrum-based neural-net connection admission control (PNCAC) method for multimedia networks. We first transform the time- domain parameters of source traffic of connections into the power-spectrum parameters in the frequency domain, then a decision hyperplane of the connection admission control is constructed under the constraint of QoS after the neural network has been trained. The decision hyperplane splits the sample space into two parts: one is for ‘accept’ and the other is for ‘reject’. We further adopt the learning/adapting capabilities of the neural network to adjust the optimal location of the boundary between these two decision spaces (i.e. using the back-propagation training algorithm to adjust the link weights of PNCAC to the optimum value). Simulation results show that PNCAC achieves higher system utilisation, superior by 23 3% to the conventional equivalent capacity CAC proposed in [2], and comparable to that of Hiramatsu’s neural network CAC (”CAC) [9]. However, PNCAC is more robust than Hiramatsu’s NNCAC in high-speed multimedia networks. As characteristics of traffic sources change, the connection number of each traffic type utilised as the input variables in Hiramatsu’s NNCAC can no longer characterise the traffic. At this time, Hiramatsu’s NNCAC should perform online training and even the node-growing or node-pruning learning process to adapt to the variation in traffic sources, otherwise, the performance would deeply degrade with the QoS no longer guaranteed. However, the proposed PNCAC can still perform well without any other modifications or retraining process.

2

If an input rate process u(t) is modelled as an ( M + I)-state Markov-modulated Poisson process (MMPP), the MMPP can be represented by (Q, r): where Q is the state transition- rate matrix and r = [yo, yl,

.

. .

, y M ] is the vector representing the arrival rate at each MMPP state. The stationary probability vector of state, denoted by

fZ

= [no, 711,.

. .

, n ~ ] ,

can be obtained by solving equations of nQ=O and

ne

= 1, where e is an unit column vector. The average input rate

-7

is then given by

Power spectrum of the input process

M

7

= CYiTi i=O

Q is diagonalisable and can be represented by spectral decomposition as

M

where AI is the lth eigenvalue of Q, and g, and hl are the associated right column and left row eigenvectors of Q with respect to

L,,

respectively [6].

Then the autocorrelation function of the MMPP, defined as R ( z )

=

n ( t ) a ( t

+

z), can be derived. Its corresponding

PSD, denoted by

P(o),

can also be given, via Fourier transformation of R(z), by [6]

M

P ( w ) =

y

+

27rYo6(w)

+

bl(w) ( 3 )

/= 1 where

Y o is the DC component, given by

y o = 7 2 ( 5 ) and b/(co) is the bell-shaped function with respect to nonzero

AI,

given by

Y , in (6) is the average power contributed by

I,/,

given by

where glL and h, are the ith andjth entities of the vector g1 and hl, respectively. Bl in (6) is the half-power bandwidth, Bl= -2Re{4} and the col in (6) is the central frequency of the bell-shaped function b/(o), o/= fin{Al}, where Re{ . } and

Zm{

. } denote the real part and the imaginary part of the argument, respectively.

From (3), it can be found that the PSD of an MMPP process is constituted by white noise

7,

DC component 2nY0, and a set of bell-shaped functions bl (a) described by the average power \ V I , the half-power bandwidth Bl and the central frequency w ~ , with respect to the lth eigenvalue of Q. The white noise is contributed by the Poisson local dynamics. From the result demonstrated in [5], the influence of the white noise on a queueing system can be neglected.

If the traffic source is further assumed to be an

(Mi-

1)- state birth-death MMPP, which is a superposition of A4 independent and identically distributed (i.i.d.) two-state MMPPs with parameters (a,p,r,) as shown in Fig. 1 , it would have all eigenvalues real and all bell-shaped fLmtions zero-centered. Take a two-state MMPP for example, its time-domain traffic parameters described by (a,

p,

r.,) are shown in Fig. 2 u, and the PSD parameters characterised by

(7,

B , Y ) are shown in Fig. 2b, where

7

= / h , / ( a

+

/)),

B = 2(a

+

p)

and Y = apro/(a+p)’. The PSD of the ( M + 1)-state birth-death MMPP can be obtained by composing PSDs of the M i.i.d. two-state MMPPs into a composite power spectrum which is further approximated by an impulse DC component and a single bell-shaped function with parameters

00 f o r w = 0 0 elsewhere

S(w) = ₍₄₎ The composition algorithm for the two different power spectra is stated in the Appendix.

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, a b

Fig. 2 Tii~.le~reclzieiic~-~l~)inain parmeters of the two-state MMPP

Therefore, it can be concluded that a birth-death MMPP

traffic source can be described by its PSD with power- spectrum parameters

(?,

B , !P) including the DC component

(y),

the half-power bandwidth (B) and the average power

(Y)

of the bell-shaped function. These parameters can be obtained from the ( M + 1)-state MMPP parameters (a, [j, ro). The larger the mean input rate, the higher

v

will be, the more correlated the input process is, the smaller B will be and the larger the input rate variance is, the higher Y will be. Moreover, the PSD parameters of the input process possess the additive property, which does not exist in the time-domain traffic parameters.

When a new call request provides its time-domain traffic parameters such as peak bit rate (RP), mean bit rate (RM) and average peak bit rate duration (TD) during the call establishment phase, the modelled ( M + 1)-state birth-death MMPP process with pardmeters (u, /3, ro) can be obtained from these traffic parameters ( R p ,

RM,

7‘’) by

RP r, = -

M

The power-spectrum parameters

(7,

B , Y ) of the input traffic of the new call can then be converted from the ( M + 1)-state birth-death MMPP parameters (a,

/3,

ro) by (8)H 10).

new call request for voice and video

(R,u 1 Rp 8

L)

new call request

for data

time/frequency parameter

converter

I

3 PSD-based neural-net connection admission controller

Fig. 3 shows the functional block diagram of the PSD- based neural-net connection admission controller. It mainly contains a PNCAC controller, a time/frequency parameters converter, a data rate register, a PSD parameter register, a data rate composer and a power spectrum composer. Input traffic is assumed to be classified into two types. Type-1 traffic is the real-time traffic such as voice and video, and type-2 traffic is the non-real-time traffic such as data.

As the new call request for type-] traffic claims its traffic parameters, Rp, RAl and T D , in the call establishment phase, the time/frequency parameter converter transforms the (RM, Rp, TD) in the time domain into

(?,

B , Y’) in the frequency domain. The PSD parameter register keeps the record of the power-spectrum parameters

(YE,

B E , Y E ) of the total existing type-1 connections, where

Y E

is the total average input rate, BE is the total half-power bandwidth and YE is the total average power. The two sets of

parameters

(7,

B , Y ) and ( ? E , B E , Y E ) are added to form a new set of parameters

( V T ,

B T , Y T ) through the power spectrum composer which performs the power spectrum composition and approximation functions mentioned in the Appendix. If the new call request belongs to type-2 data traffic, it claims the data rate

r

as the traffic parameters in the call establishment phase. The data rate register records the overall data rate

rE

of the existing type-2 connections, and the data rate composer adds these two data rates,

r

and fE, to form a new parameter fT. The set of PSD

parameters

( y T ,

B T , Y T ) accompanied by the data rate f is then fed into the PNCAC controller as the input variables. As shown in Fig. 4 , the PNCAC controller is a multilayer feedforward neural network [lo, 121, which possesses capabilities of approximation to a perfect connection acceptance decision fhction. A back-propagation learning algorithm [13] is used here to train the neural network. The PNCAC controller will then decide whether to accept or reject this connection request using the neural network and feed the decision output (r) back to the source.

If the decision is lo accept the new type-1 call, the PSD parameter register will be triggered to update the stored power-spectrum parameters

( V E , B E ,

Y E ) to be

( V T ,

B T , Y r ) . Similarly, so does the type-2 data rate register if a type-2 call is accepted. If the decision is to reject the new call, no updating procedure is needed. Notice that

(7,

B ,

Y)

data rate

PNCAC controller

-

accept / reject

decision

Fig. 3 Functional block diagram of the PSD-based neiiral-net connection ndnzission controller

Y

(4)

I I

or

r

should be subtracted from

(T,;,

Bb:, Y E ) or l’,; when a

type-I or type-2 call is disconnected, respectively, which is not shown here.

The impleiiieiitatioii of the proposed PNCAC takes about 200 lilies of C codes, in which 370 inultiplication and 3 10 addition operations are included. The coniputatioii time to make an admission decision would be no more than

500 ps under general purpose CPU such as Intel Pentium-TI or abovc. Tlierefoi-e, tlie PNCAC would be feasible in real iiiipleinentation for high-speed multimedia networks. If special purpose CPU or DSP processors with pipeliiic architecturc or optiniised computation capabilities are adopted, less tiine should be taken to respond to a call request. Also, the compiled inachiile (execution) codes for Intel CPU occupy about 20Icbytc. The proposed PNCAC scheme can even be downloaded to the embedded system (platforms).

4 Simulation results and discussions

Here we assume that the call admission controller is designed in an ATM switcli/router in multimedia networks, and input messages are segmented into fixed-length ATM cells. Two separate buffers with buffer size K1 and K2 are for type- I and type-2 traffic, respectively. One buffer space can accommodate one ATM cell. When the buffer is firll, new coming cells are blocked and lost. The service disciplinc for type-l and type-2 traffic is that the system initially allocates equal capacity for both types, and the remaining capacity of one type of traffic can be used by the other type of traffic.

In the simulations, the buffer sizes K I and K2 are all set

to be 100 cells; the systcin capacity is assuined to be 150 Mbit/s. Different QoS requirements for these two types of traffic are defined: the required cell loss probability is set to be 10

’

for type-I traffic and IOp6 for type-2 traffic. The voice so~irccs are modelled by a two-state on-off

Markov

chain (MMPP); the video soiirces are modelled by a modified Markov process addressed in [Ill, where tlie numbers of video interframes and intrafmmes are assumed to have five states, and thc data sources are modelled by a Poisson process. The traffic parameters for voice and video sources are shown in Table I, and the mean 1-ate for data sotirces is 1 Mbit/s. The call arrival rate for voice is 15.4

calls/s with mean holding time of one minute, the call arrival rate for video is 0.082 calls/s with mean holding time of five minutes, and the call arrival rate for data is 3.2 calls/s with mean holding time of 20 s. For all traffic types, the call arrival processcs are ass timed to be independcntly Poisson distributed, and the mean holding time is assunicd to be exponentially distributed. Note that in the transforination of the three input time-domain parameters (R,,,,, R p , T,)

Table 1: Traffic source parameters

Traffic Peak rate Mean rate Peak rate

parameters duration

Voice 64.0 kbit/s 27.6 kbit/s 1.366 s

Video 5.7 kbit/s l.SMbit/s 0.033 s

Data 1 .O Mbit/s

into PSD parameters

( 7 ,

B , Y’), both voice and video so~~rces are assumed to be two-state birth-death MMPP.

The neural networks adopted by the PNCAC is a thrce- layered fully-connected feedforward neural nctworlc with 50 hidden nodes, as the one used by Hirainatsu’s NNCAC which has 30 hidden nodes. It L I S ~ S 683 and 280 training data and tales about 221467 and 199501 itcrations to

thoroughly train tlie PNCAC and Hiramatsu’s NNCAC, respective1 y.

Fig. 5 shows tlie cell loss ratio of type-1 and type-2 traffic, and tlie system utilisation in Figs. 50, h and c respectively, for the three approachcs, where the characteristics of traffic source in simulation are exactly the same a s the ones used in tlie ti-aining data generation phase. We can find that, after the neural networks have been well trained, both Hiramatsu’s NNCAC and PNCAC have larger cell loss ratio than ECCAC, but still guarantee QoS require- ments, while Hiramatsu’s NNCAC and PNCAC can improve significantly the systcni ntilisation over the conventional ECCAC by about

24.4%

and 23.8%, respectively. Note that this iiti1is;ition is obtninccl by averaging those values between 10‘) and 2 x IO9 slot timcs. This is because of the learning and adaptive capability of neural networks. Also, Hiramatsu’s NNCAC has slightly better system utilisation than PNCAC by about 0.6‘%, a s

Hinamatsu’s NNCAC adopts the connection number of each traffic characteristic 21s the input to decide whether ;I call request is accepted or not, aiid the traffic characteristics

in siinulations are exactly the same as the oiics used in the training data generation phase for Hirmiatsu’s NNCAC.

We further consider two simulation examples when thc neural networks were well traincd according Lo the traffic charactcristics illustrated in Table 1 , but the system receives heavier and lightcr traffic sources with paramcters in Tables 2 and 3, respectively.

shows the cell loss ratio of type-1 and type-2 traffic, aiid the system Litilisation, for the heavier traffic source, in Figs. 6u. h aiid c, respectively. It can be seen that the cell loss ratio of Hiramatsu’s NNCAC, denoted by the dashed line, seriously violates the QoS requirements, in both type-1 and type-2 traflic, although tlic utilisation of Hiramatsti’s NNCAC is tlie highest onc and approaches l000/~1. However, the proposed PNCAC xnd ECCAC can still fulfil the QoS requirements, and tho system Litilisations of PNCAC and ECCAC are 85.8%) and 77.7‘!4, respectively.

shows the cell loss ratios of type-1 and type-2 traffic, and tlie system utilisation, for the lighter traffic so~irce, in Figs. 7 ~ , h, and c, respectively. I t can be seen that all the three CAC schemes havc zcro cell loss ratios and guarantee the required QoS but obtain low system utilisations, conipared to those of the normal case shown in Fig. 5 . Hiramatsu’s NNCAC suffers more degradation

From t h e two simulation examples, it can be concludcd that Hiramatsu’s NIVCAC has worse adaptivity and flexibility than PNCAC and ECCAC. This is because the connection number of each traffic type adopted by

Fig. 6

Fig. 7

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400 800 1200 1600 2000 time slot ( X I O ~ ) a

I

y- 0.8

-

: t

PNCAC 0.2 0 400 800 1200 1600 2000

time slot (XI 0') b 1 .o 0.9

5

0.8 .- a 5 0.7 .-

-

.- 0.6 0.5 Hiramatsu NNCAC - ECCAC

---.L-

.--.-.--.-- I I I I I I I l I 400 800 1200 1600 2000 time slot ( x i 0 6 ) C Fig. 5

u Type-I cell loss ratio (CLR)

b Type-2 cell loss ratio (CLR)

c System utilisation of the ECCAC, Hiramatsu's NNCAC, and PNCAC

Cell loss ratios and system utilisution

Table 2: Heavier traffic source parameters

~ ~~~~~~

parameters duration

Video 1 1.4 M bit/s 3.8 Mbit/s 0.033 s

Data - 1.5Mbit/s -

Hiramatsu's NNCAC could apply only when the traffic characteristics of traffic sources fed into the operational system are the same as the ones in the training phase. However, this is usually impossible in real practice. As

Table 3: Lighter traffic source parameters

parameters duration

Video 2.85 Mbit/s 0.95 Mbit/s 0.033 s

Data - 0.5 Mbit/s ~ 1 .o 7- 0.8

z

.E 0.6 F -0 0.4 v m

-

- (u 0.2 0 I I I I I I I I I Hiramatsu NNCAC j

1

PNCAC

b

400 800 1200 1600 2000

time slot (XIO')

a

5 1-

Hiramatsu NNCAC

1

0 _PNCAC

ECCAC

400 800 1200 1600 2000

time slot (XIO~) b . . . -a 0.9 Hiramatsu NNCAC 400 800 1200 1600 2000

time slot (XIO')

C

Fig. 6

a Type-1 cell loss ratio (CLR)

b Type-2 cell loss ratio (CLR)

c System utilisation of the ECCAC, Hiramatsu's NNCAC, and PNCAC with heavier traffic sources

traffic characteristics of sources change, the neural network should learn to adapt to the variation in sources by online training, and moreover, the structure of the neural network should be modified to have proper inputs by a node- Cell loss rutios und system utilisution for heuuier trqffic Sources

I.!?E PVOC C O ~ l ? ~ 7 ~ L i t l . , V d 149, NO. 2, ftlJVi/2002 14

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. ; 0.6 L u) P 0.4 - - a, 0.2 r- 0.8 2 0.6 m - -

-

9

. " I

0.4 1 .o 0.9 0.8 0.7 5 0.6 .-

"

0.2 I I I I I I I I I - -

c

PNCAC - - ECCAC, Hiramatsu

f

NNCAC. PNCAC ? ; 0.8

1

r v X ECCAC, Hiramatsu NNCAC, PNCAC

growing or node-pruning learning process, if necessary. This would make Hiramatsu's NNCAC infeasible. Because both ECCAC and PNCAC depend on traffic characteristic parameters which can react to the variation in traffic characteristics, these two schemes can adapt to traffic properly without any other modifications or retraining and still perform the CAC decision well. It is also because the transformed equivalent capacity for ECCAC and the PSD

parameters for PNCAC are both unified metrics corresponding to traffic characteristics of all different sources and possess the additive property, while the connection number adopted by Hiramatsu's NNCAC as the input variables for neural networks could not be suinnied for different traffic types. 6 m- 0 E 5 1 0 -15 -10 -5 0 5 10 15 frequency (I)

Fig. 8 Appoxiniated hell-shnyed,fuizction

(i) Approximated bell-shaped function h(w) (ii) Composite power spectrum hl(ci))

+

h2(w)

(iii) Bell-shaped function 6,(w) (iv) Bell-shaped function b2(w)

In addition, the proposed PNCAC has better performance than ECCAC. Both PNCAC and ECCAC depend on traffic characteristic parameters. However, PNCAC transforms the three time-domain traffic characteristic parameters into the corresponding three PSD-domain parameters, while ECCAC converts the same tinie-domain parameters to a single equivalent capacity. Although the equivalent capacity is also additive, the proposed PNCAC adopts the three PSD parameters as the inputs of neural networks to perform the CAC decision, which could capture more traffic characteristics and less composition approximation error than the single equivalent capacity. The self-learning capability of neural network also makes the PNCAC more adaptive to the traffic.

5 Concluding remarks

In this paper, we propose a power-spectrum-based neural- net connection admission control (PNCAC) scheme for multimedia networks. The PNCAC method adopts the converted power-spectrum parameters of traffic sources to represent its traffic characteristics and uses a neural network to implement the connection admission control. The frequency-domain power-spectrum parameters of traffic sources possess the additive property and can capture the correlation and burstiness behaviour more than the time- domain parameters such as peak rate, mean rate and peak rate duration. The neural network has learniiig/adapting capabilities so that the boundary of the decision hyperplane for the connection admission control can be adjusted optimally and dynamically. We demonstrate results when- ever the input voice and video traffic sources are modelled by MMPP and modified MMPP, respectively, and the data traffic sources are modelled by a Poisson process. Simula- tion results show that the proposed PNCAC enhances significantly the system utilisation while fulfilling QoS requirements. Not only is it superior to the conventional equivalent capacity CAC scheme (ECCAC), but it also obtains more flexibility and robustness than Hiramatsu's NNCAC.

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6 Acknowledgments

This work was supported by the National Science Council, Taiwan, under contract numbers 88-221 3-E-009-088 and 89-2213-E-009-105 and by Lee and MTI Center for Networking Research at National Chiao Tung University, Taiwan. 7 I 2 3 4 5 6 7 8 9 IO References

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Chap. 8

Appendix: Composition algorithm for power spectra

Assume that h , (w) and b2(o) are two bell-shaped functions corresponding to zero-centred PSDs with parameters

(TI

B I , Y I ) and

(y2,

B z ,

!Pz),

as shown iii Fig. 8 , and that h(w) is the approximated bell-shaped function correspoiid- ing to the composite power spectrum with parameters

(7,

B , Y). To compose the two zero-centred PSDs, we add the two DC components aiid the two bell-shaped functions directly. We then approximate h,(w) +02(o) to be b(cd). Tii the approximation, we set Y = Y I

+

!P2, and h(w) = h,(w) h2(w) at o = 0. Therefore,

(7,

B , ‘U) of the approximated power spectrum are given by

+:12 (14)

Y = !PI Jr Y2

Note that the approximated bell-shaped filiictioii coiitaiiis more low-frequency components than bl(w)

+

b2(o).

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