A. INTRODUCTION

In integrated-service, packet-switched networks,packets from different sessions belonging todifferent applications interact with each other whenthey are multiplexed at the same output link of aswitch. Different applications expect differentservice requirements and the deployment of priorityalgorithms may be a key component in controllingthe interactions among different traffic flows [1, 2].This technical report describes a Fuzzy Logic-basedpriority control mechanism that is an extension ofthe one proposed in [3]. The fuzzy system has beenre-designed with two aims:� Enhancement of performance in an ATM

environment as compared with the solutionproposed in [3];

� An extension allowing control to be applied topacket-switched networks operating withvariable-sized packets, such as the Internet.

There are various real applications for our proposedsystem, for example in ATM switches, in the bufferof a generic virtual path, when the network isoperating in a CLP-significant mode, i.e. the QoSrequirement in terms of cell loss probability onlyapplies to the high-priority flow and the network canmake a best-effort attempt to transmit the low-priority flow. Again, to meet the demand for QoS inthe future Internet, link-sharing mechanisms allowmultiple agencies or organizations to receive aguaranteed share of the resources (buffer and linkbandwidth). If the real-time traffic (guaranteedflows) for an agency has little data to send, ourpriority control scheme allows excess bandwidth tobe exploited to transmit the agency’s best-efforttraffic.The aim of the priority control function beingstudied is therefore to maximize network utilizationwithout degrading the QoS for high-priority traffic.The priority control mechanisms have to be flexible

so as to adapt to different types of traffic. Inaddition, as the priority algorithms have to act onthe forwarding path of the switch, they cannot beexcessively complex so that they can be executed asrapidly as possible. The solutions proposed so far inthe literature have proved to be unsatisfactory eitherbecause they are difficult to implement or becausethey do not ensure a high level of performance(push-out and threshold mechanisms) [4, 5]. Duringthe research carried out, we defined an innovativepriority control scheme based on fuzzy logic, whichrespects the QoS of high-priority traffic andcombines flexibility requirements with optimizationof resource utilization. The report is organized asfollows: Section 2 describes the new version of thefuzzy priority control system; Section 3 presents anassessment of the performance of the system and adiscussion about his extension to Internet; Section 4proposes a possible implementation of the system inVLSI technology.

B. MODEL OFFUZZY PRIORITY CONTROL

SCHEME

In this section, we will describe a new version of theFuzzy Priority Control (FPC) mechanism proposedin [3] which meets the requirements of performance,flexibility and cost-effective implementation of ahigh-speed packet-switched network based onATM. We will consider a cell-based switch outputbuffer (with finite size and constant emptyingcapacity) integrating high-priority traffic, withsevere QoS requirements, and low-priority, “besteffort” traffic. The aim is to prevent the low-prioritytraffic from degrading the QoS of high-prioritytraffic.For the FPC scheme not to become a bottleneck wechose to make it work only at the buffer input todecide whether to accept or reject any new low-priority cell, and the discarding of low-priority cellsalready in the buffer is not allowed (see Fig. 1).

V. Catania, G. Ficili, D. Panno

A FUZZY SYSTEM FOR PRIORITY CONTROL IN PACKET-SWITCHEDNETWORKS

Istituto di Informatica e Telecomunicazioni,University of Catania - ITALY

Figure 1

The quality of service is expressed in terms of theCell Loss Ratio Requirement for High-priority trafficflows (CLRRH). As the aim of the FPC scheme is toguarantee this requirement for high-priority cellsand exploit the network when it is underloaded, asthe input parameters for our fuzzy system we chosethe Cell Loss Ratio experienced in the buffer byHigh-priority traffic (CLRH) and the state ofoccupation of the buffer. The latter is described bythe number of cells in the buffer (N) and the rate atwhich the length of the queue in the buffer varies(∆N), which lets us discriminate between situationsin which the state of the network evolves towardslow traffic intensity and those in which it evolvestowards congestion.The three input parameters, CLRH, N and ∆N, areconsidered to be linguistic variables each having aterm-set with a greater cardinality than the onedetermined in [3]. The membership functions chosenfor the fuzzy sets and the fuzzy names used areshown in Figs. 2, 3, and 4. Note that themembership functions are parametric with CLRRH,the cell loss ratio requirement negotiated for thehigh-priority traffic flow, and with Q, the size of thebuffer in bytes, and they do not depend on the trafficparameters. This is a important condition for theflexibility of our mechanism.

1.0

0.0

Low Medium High

0.6 PLRRH 1.00.7 PLRRH 0.8 PLRRH

Very High

PLRRH0.0

Figure 2: Membership functions for the CLRH inputvariable

The term set of the output variable ACTION iscomposed of 6 fuzzy sets whose fuzzy names are:Strong Discard (SD), Discard (D), Marginal Discard(MD), Marginal Admit (MA), Admit (A) and StrongAdmit (SA). The membership functions are show inFig. 5.

1.0

0.0

Low Medium High

0.05 Q Q0.1 Q 0.15 Q

Very High

0.25 Q 0.4 Q0.0

Figure3: Membership functions for the N inputvariable.

1.0

0.0

Pos. SmallZero

0.1 Q Q-0.1 Q 0

Neg. Big

-Q -0.2 Q 0.2 Q

Neg. Small Pos. Big

Figure 4: Membership functions for the∆N inputvariable

0.0

1.0 SAA

0.4

MADSD

10.60.2

MD

0.80.0

Figure 5: Membership functions for the Actionoutput variable

The inferential rules of the fuzzy system were firstwritten on the basis of intuitive considerations andthen tuned by simulation tests. To give high-priorityflows a better guarantee of their QoS, the rules werewritten assuming that an arriving cell is of themaximum length (conservative assumption).The fuzzy rules for the system are shown in Tab. 1;by way of illustration, rule 1 has to be read asfollows:

If CLRH is Low and N is Low and∆N is Negativethen the Action is Strong Admit.

The inference method chosen was Max-Min and theYager method was used for defuzzification.The fuzzy rules defined are easy to understand andare highly suitable for representation of the decision-making process a priority control mechanism has topossess. The philosophy behind the knowledge baseof the FPC scheme is that of admitting low-priority

cells when they do not affect the high-priority flow.This happens either when the CLRH is considerablylower than the CLRRH and the value of N is not high(rules 1-10) or when, although the CLRH is close tothe CLRRH values, the network resources aretemporarily underloaded, i.e. the value of N ismedium or low (rules 21-30, 41-45, 61-65). Viceversa, in congested conditions where the CLRH isvery high (rules 66- 80), or in risk conditions, wherethe state of occupation of the buffer indicates apossibility of congestion because N is high or veryhigh and/or∆N is positive small or big, the action ofthe Fuzzy Priority Control has to be unfavorable tolow-priority cells (rules 16-20, 36-40, 56-60). Allthe other rules represent intermediate situationsbetween these two, thus providing the controlmechanism with a highly dynamic action.

# Rule CLRH N ∆∆∆∆N Action1. L L NB Str. Adm.2. L L NS Str. Adm.3. L L Z Str. Adm.4. L L PS Str. Adm.5. L L PB Str. Adm.6. L M NB Str. Adm.7. L M NS Adm.8. L M Z Marg. Ad.9. L M PS Marg. Ad.10. L M PB Marg. Ad.11. L H NB Adm.12. L H NS Marg. Ad.13. L H Z Marg. Ad.14. L H PS Marg. Disc.15. L H PB Marg. Disc.16. L VH NB Marg. Disc.17. L VH NS Marg. Disc.18. L VH Z Marg. Disc.19. L VH PS Disc.20. L VH PB Disc.21. M L NB Str. Adm.22. M L NS Adm.23. M L Z Adm.24. M L PS Adm.25. M L PB Marg. Ad.26. M M NB Adm.27. M M NS Adm.28. M M Z Marg. Ad.29. M M PS Marg. Ad.30. M M PB Marg. Ad.31. M H NB Marg. Ad.32. M H NS Marg. Ad.33. M H Z Marg. Disc.34. M H PS Marg. Disc.35. M H PB Marg. Disc.36. M VH NB Marg. Disc.37. M VH NS Marg. Disc.38. M VH Z Disc.39. M VH PS Disc.40. M VH PB Str. Disc.

# Rule CLRH N ∆∆∆∆N Action41. H L NB Adm.42. H L NS Adm.43. H L Z Marg. Ad.44. H L PS Marg. Ad.45. H L PB Marg. Ad.46. H M NB Marg. Ad.47. H M NS Marg. Ad.48. H M Z Marg. Ad.49. H M PS Marg. Disc.50. H M PB Disc.51. H H NB Marg. Ad.52. H H NS Marg. Disc.53. H H Z Disc.54. H H PS Disc.55. H H PB Disc.56. H VH NB Marg. Disc.57. H VH NS Disc.58. H VH Z Disc.59. H VH PS Disc.60. H VH PB Str. Disc.61. VH L NB Marg. Ad.62. VH L NS Marg. Ad.63. VH L Z Marg. Ad.64. VH L PS Marg. Ad.65. VH L PB Marg. Ad.66. VH M NB Disc.67. VH M NS Disc.68. VH M Z Disc.69. VH M PS Str. Disc.70. VH M PB Str. Disc.71. VH H NB Disc.72. VH H NS Disc.73. VH H Z Str. Disc.74. VH H PS Str. Disc.75. VH H PB Str. Disc.76. VH VH NB Str. Disc.77. VH VH NS Str. Disc.78. VH VH Z Str. Disc.79. VH VH PS Str. Disc.80. VH VH PB Str. Disc.

TABLE I : INFERENTIAL RULES OF THEFPCSCHEME

C. PERFORMACEEVALUATION

This section reports on an assessment of the FPCscheme by simulation. The measures used for theassessment include the cell loss ratio experienced byhigh-priority cells and the throughput of theaggregate flows (high- and low-priority flows). Thesimulations use a single-server queuing system witha FIFO service discipline to model the multiplexingbuffer. We assume a finite buffer, Q=100 cells, and aconstant service rate, C = 10000 cell/s.We tested the FPC in different load conditions andwith different types of traffic: packetized voice andreal video sequences, including video clips, movies,cartoons and sports events, encoded by the MPEGcoding scheme, for the high-priority flows; andbursty data traffic for the low-priority flows.Fig. 6a shows the CLRH for the high-priority flowsversus the percentage of low-priority loadnormalized with respect to C, assuming the high-priority load to be constant, equal to 55 % of C. Inthe simulation we assumed CLRRH = 10-3 as the QoSrequirement for high-priority traffic. Although thisvalue is higher than the one required by videoservices, we chose it in order to obtain reliableresults in practical simulation times. Note that, in thecase being investigated, when there is no low-priority load, the CLRH for high-priority traffic islower than the requirement negotiated CLRRH. Forthe low-priority load we considered multiplexedbursty homogeneous traffic flows with a peak bitrate equal to 0.05 normalized on C, and variableexponentially-distributed activity (TON) and inactivity(TOFF) times with a mean value of 64⋅10-2 sec and12⋅10-2 sec respectively.

0,0E+00

2,0E-04

4,0E-04

6,0E-04

8,0E-04

1,0E-03

1,2E-03

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45

Low-priority load offered

CLR

for

high

-prio

rity

traf

fic

CLR requirementpush-outfuzzy priorty controlbest-thresholdno low-priority traffic

Figure 6a: CLRH for high-priority traffic.

0,50

0,60

0,70

0,80

0,90

1,00

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45low-priority load offered

Tot

alT

hrou

ghpu

t

push-outbest-thresholdfuzzy prority controlno low-priority traffic

Figure 6b Total throughput

Fig. 6b shows the total throughput normalized to Cversus the percentage of low-priority load for thesame simulation runs. As can be seen, the FPCscheme considerably increases the throughput withrespect to when low-priority traffic is not admitted;this is to the advantage of network efficiency anddoes not penalize the CLRRH.To compare the behavior of the FPC scheme, in thefigure we also show the results obtained when theswitch uses the push-out control scheme [3], whichsupplies an upper bound for the maximumthroughput that can be achieved. Additionally towhat was done in [3], the FPC is also comparedwith an ideal best-threshold mechanism. The resultsfor the latter were obtained by adapting thethreshold value in a fixed-threshold mechanism tothe load conditions.As can be seen in Fig. 6a, although the CLRRH

requirement is met with any mechanism, the cell lossexperienced with the FPC is significantly lower thanthat of the push-out mechanism and comparablewith that of the best-threshold scheme. In practice,however, fixed-threshold mechanisms are notapplicable, even though they are simple toimplement, because to achieve the results given inthe figure it would be necessary to choose anoptimal threshold value for each load condition. Thislack of flexibility is not shown by the FPC: being afuzzy system it dynamically adapts its control actionto the different load conditions. It should be pointedout that the results obtained with the FPC do notsignificantly penalize the increase in throughput,which is only slightly lower than the maximumthroughput obtained with the push-out mechanism(see Fig. 6b).To evaluate the robustness of the fuzzy systemproposed, we stressed the control under heavy-loadtraffic conditions, i.e. we simulated control whenthere is a high percentage of high-priority load

(70%) and the Cell Loss Ratio experienced in thebuffer is very close to the QoS required. In Fig. 7,the results show that in this condition the FPCscheme guarantees the CLRRH; vice versa, when thepush-out algorithm is applied, the presence of thelow-priority load is not transparent to the high-priority load: the CLR requirement is, in fact, notmet. When the threshold mechanism is used, therequirement is obviously not violated because, assaid previously, the values were obtained byadapting the threshold value.

0,0E+00

5,0E-04

1,0E-03

1,5E-03

2,0E-03

2,5E-03

3,0E-03

3,5E-03

0 0,05 0,1 0,15 0,2 0,25 0,3

Low priority load offered

CLR

for

high

prio

rity

traf

fic

CLR requirement

no low-priority trafficpush-out

best-thresholdfuzzy priority control

Figure 7a: CLRH for bursty high-priority traffic inheavy-load conditions.

0,6

0,7

0,8

0,9

1

0 0,05 0,1 0,15 0,2 0,25 0,3

Low priority load offered

Tot

alT

hrou

ghpu

t

push-outbest-thresholdfuzzy priority controlno low-priority traffic

Figure 7b: Total throughput in heavy-loadconditions

Fig. 7b shows the total throughput versus thepercentage of low-priority load for the samesimulation runs. As can be seen, the FPC schemeagain considerably increases the throughput ascompared with the case in which low-priority trafficis not admitted, thus enhancing network efficiencywithout penalizing the CLRRH. The total throughputwith the push-out scheme grows even more, but thisis in reality due to an increase in the throughput forlow-priority cells and a decrease in the throughputfor high-priority cells.We also stressed the fuzzy control scheme withdifferent statistical characteristics for low-prioritytraffic. The results obtained are not given becausethey are very similar to those shown in Figs. 6 and 7.

Finally we assessed the performance of the FPC byconsidering a different CLRRH requirement, 10-4.The results obtained, shown in Figs. 8a and 8b,demonstrate that the FPC scheme performs as in theprevious cases.

0,0E+00

5,0E-05

1,0E-04

1,5E-04

2,0E-04

2,5E-04

3,0E-04

3,5E-04

4,0E-04

0 0,05 0,15 0,25 0,35 0,45 0,55

Low priority load offered

CLR

for

Hig

hpr

iorit

ytr

affic

CLR requirement

push-out

best-threshold

fuzzy priority control

Figure 8a: CLRH for high-priority traffic having theQoS requirement CLRRH = 10-4.

0,4

0,5

0,6

0,7

0,8

0,9

1

0 0,05 0,15 0,25 0,35 0,45 0,55

Low-priority load offered

Tot

alth

roug

hput

push-outbest-thresholdfuzzy priority controlno low-priority traffic

Figure 8b: Total Throughput for CLRRH=10-4.

In conclusion, the simulation results clearly showthat the new fuzzy system outperforms the versionproposed in [3], as it rigorously guarantees theCLRRH value, even in heavy load conditions, butdoes not penalize the increase in throughput.Currently, we are studying an extension of thepresented mechanism to an Internet environment inwhich packet are of variable length. We refer toadvanced IP routers which internally operate on dataof fixed size; in this case, input IP datagrams aresegmented into ATM cells, processed by a cell-based switching fabric and delivered to appropriateoutput interface where the cells are reassembled inthe original IP datagrams.We assume that some router resources (i.e. buffermemory and link bandwidth) have been reserved byappropriate reservation protocols to high-prioritytraffic. Low-priority packets are allowed to enter theallocated buffer to improve the exploitation ofreserved resources. The reference model is made upby a packet stream in which are multiplexed highand low priority packets. The input packet streamcould represent the traffic transported by a

connection in which the existence of low-prioritypackets could be due:• to the tagging action of traffic enforcement

mechanisms [6];• to the traffic of an agency a certain QoS is

guaranteed to; the agency could exploit theallocated resources by multiplexing flows withtwo priorities.

In our model we assume that all the cells of anarriving packet (cell bulk) are simultaneouslypresented to the buffer input. The admitting policyhas to decide if to admit all the cells of the bulk ordiscard them. This policy prevents the waste of thenetwork resources which would be caused iffragments of a packet are allowed to enter the bufferas the packet, however, needs to be retransmitted.To take into account this policy, we introduce a fewsimple modifications to our control mechanism. Weonly need to modify the estimation of buffer state bykeeping the knowledge base unvaried. In particular,the decision of admitting an arriving low-prioritypacket, with lengthx, is taken by inferring theoutput with the assumption that the buffer state (Nand ∆N values) is updated as ifx-1 cells of thepacket have been already admitted. If the inferenceresult is no admission then all the cells of the packetare discarded and the buffer state is restored to theprevious values. With this modified version of thecontrol system, the first simulation results obtainedconfirm the validity of the proposed fuzzy scheme byensuring both the respect of QoS of the high-prioritytraffic and an increasing in throughput close to push-out one.

D. REMARKS ON IMPLEMENTATION OF THE

FUZZY PRIORITY CONTROL

One of the most important requirement a controlmechanism for high-speed networks has to possessis that of easy implementation. The push-out, asremarked previously, is very difficult to implementwhile the threshold mechanisms, of immediateimplementation, unfortunately, do not present anyflexibility in adapting to different traffic loadconditions. In this section, we will give someelements to evaluate the complexity and costs theFPC mechanism entails if a hardware implementationis chosen. By way of an example, we refer to an

ATM access switch in which several sources aremultiplexed in a virtual path buffer.To define the features of the hardware system, weanalyze the requirements, expressed in terms oflatency and processing capacity, made of the fuzzycontrol scheme in controlling the priority of a trafficflow entering the buffer. They depend on thestatistical characteristics and the number ofmultiplexed sources.First let us focus on the control of a single sourceflow characterized by a minimum cell interarrivaltime of tc=1/PCR, where PCR is the peak cell rate.The action of the FPC scheme has to be real-time, inthe sense that a decision has to be made on-line foreach low-priority cell arriving in the buffer. Itfollows that tc is the upper bound for the latency, tL,of the hardware system, that is the maximum timelimit by which the FPC system has to infer theoutput by processing the 80 rules of the KnowledgeBase.For instance, a packetized voice source with a peakbit rate of 32 kb/s requires a performance of tL≤12ms, while for a still picture source, with a peak bitrate of 2 Mbit/s, the maximum latency should betL≤192µs.The number of sources which can be controlleddepends on the processing capacity of the FPCsystem, NINF, expressed in terms of number of FuzzyLogic Inferences that can be processed Per Second(FLIPS).In order to calculate the processing capacity of theFPC system when it has to manage M sources, let usconsider the worst case, i.e. when M multiplexedsources are simultaneously transmitting low-prioritycells at the peak cell rate and they all generate a cellin the same cell slot time.Being all the sources controlled homogeneous, thatis belonging to the same service class, they willfeasibly be scheduled in a cyclic order. Assuming anull walk time, the cycle time (i.e. the time intervalafter which a source is rescheduled) has to be equaltc. As one cell per source has to be processed withinthis time, the FPC system has to be able to executeM/tc inferences per second.As a practical example, let us calculate theprocessing capacity required to control themaximum number of admittable sources on a virtualpath in the extreme case in which its capacity equals

the ATM link transmission rate and an idealstatistical allocation criteria based on mean bit rateof sources is assumed. In these conditions themaximum number, Mmax, of connections which can

be admitted isM max =⋅C

ACR424, where 424 is the

number of bits per cell, and ACR is the Average CellRate.It follows that the maximum processing capacityrequired to the FPC system in controlling Mmax

connections is NINF = PCR ⋅ Mmax = (b⋅C)/424,where b=(PCR/ACR) is the burstiness of thesources.For instance, for a 150 Mb/s ATM link we obtainNINF = b ⋅ 0.35 MFLIPS.After discussing about latency and capacityrequirements let us address two possibleimplementation for the FPC scheme.First, we will give some elements to evaluate thecomplexity and costs the Fuzzy Priority Controlmechanism entails if a hardware implementation ischosen.The hardware approach would seem to beappropriate thanks to the high processing speedobtainable and the drastic reduction in the cost ofthe systems based on Very Large Scale Integration(VLSI) technology.Recently, there has been a spread of solutions onVLSI chips which allow fuzzy inferences to behardware-computed [7, 8]. There are also severalarchitectural proposals which allow the hardwareresources to be implemented on chips to be chosenin such a way as to obtain a certaincost/performance ratio [9, 10].Due to the different traffic types that ATM networkscan accommodate, latency and processing capacityrequirement for the FPC system spread in a widerange of values. For this reason, the hardwarearchitectures for the FPC system has to exhibit ahigh performance level, consistently with theimplementation costs.A cost-effective solution could be based on thearchitecture proposed in [10]. Its maincharacteristics are:• an efficient computational model for the

execution of fuzzy inferences.• a pipelined structure which captures the intrinsic

parallelism of fuzzy computation.

Based on these features, and exploiting the VLSItechnology advantages, the processor can achieveoptimal performance in both processing capacity andlatency. As far as the process latency is concerned, itcan be expressed (in clock cycles) as:

tL= nV⋅(T+2) + R + 2⋅log2dU

where:• T represents the number of elements in the term

set of input variables;• nV is the number of input variables;• R is the number of rules being processed;• dU represents the number of points in the

«universe of discourse».Assuming that the processor executes the inferenceof the FPC scheme, we have: nv=3, T=5, R=80,du=256. It follows that the latency tL of the FPCsystem is 117 clock cycles. With a clock frequencyof 60 Mhz, we obtain tL = 1.95µs.As the fuzzy processor is capable of executing onefuzzy rule per clock cycle, the processing capacityobtainable can be expressed as NINF =clock_frequency/R = 750 KFLIPS.It is worth pointing out that these values of latencyand processing capacity are obtained from anarchitecture which was designed ad hoc for theFuzzy Policer proposed in [10], but not optimizedfor the FPC system.At this regard, we estimated that with somemodifications on the internal architecture of thefuzzy processor and using current 0.35µm CMOStechnology, we can obtain a processing capacity ofmore than 5 MFLIPS with a latency value less than1.5 µs. This performance level guarantees that theFPC system can be successfully applied in anypractical case. In fact, with these values for latencyand processing capacity, and in the extreme case ofmean rate allocation, the hardware implementationof the FPC scheme can control traffic flows withpeak bit rate values up to 280 Mbit/sec andburstiness values up to about 15.As far as the implementation cost for the FPCsystem is concerned, with the silicon area required(less then 9mm2) and large production volumes, themonetary cost would be of a few dollars per chip.

As remarked above, the analysis presentedrepresents a worst case. As in the extended versionof the FPC scheme the traffic entering the buffer ismade up by a single stream of ATM cell bulks, the

required performance in terms of latency and FLIPSis certainly less severe than the one required by theworst case. Therefore, the proposed VLSI FPCimplementation is applicable both to the ATM andInternet environment.

E. REFERENCES

[1] ITU-TSS Recommendation I.371, “Trafficcontrol and congestion control in B-ISDN”,Frozen Issue, March 1995.

[2] R. Braden, D. Clark, S. Shenker: “IntegratedServices in the Internet Architecture: anOverview”, RFC 1633, June 1994.

[3] V. Catania, G. Ficili, D. Panno: “A fuzzy logicbased approach to multipriority control inATM networks”, Computer Standards &Interfaces,Vol. 21, May 1999.

[4] H. Kroner, G. Hebuterne, P. Boyer, A. Gravey,“Priority Management in ATM SwitchingNodes”, IEEE Journal on Selected Areas inCommunications, Vol. 9, No. 3, pp. 325-334,April 1991.

[5] K. Bala, I. Cidon, K. Sohraby, “CongestionControl for High Speed Packet SwitchedNetworks”,Proc. INFOCOM’90,1990.

[6] S. Shenker, C. Partridge, R Guerin:“Specification of Guaranteed Quality ofService, RFC 2212, September 1997

[7] K. Nakamura, N. Sakashita, N. Nitta, K.Shimomura, and T.Tokuda, “Fuzzy inferenceand fuzzy inference processor”,IEEE Micro,Vol. 13, No. 5, pp. 37-48, Oct. 1993.

[8] G. Ascia, V. Catania, “Design of VLSI parallelprocessor for fuzzy computing”,Proc. of Theeighth International Conference on VLSIDesign, New Delhi, January 1995.

[9] G. Ascia, V. Catania, “A VLSI parallelarchitecture for fuzzy expert systems”,International Journal of Pattern Recognitionand Artificial Intelligence, Vol. 9, No. 2,1995.

[10] G. Ascia, V. Catania, G. Ficili, S. Palazzo, D.Panno, “ A VLSI Fuzzy Expert System forReal Time Traffic Control in ATMNetworks”, IEEE Transactions on FuzzySystems, Vol. 5, No. 1, February 1997.