Page 111 - First special issue on The impact of Artificial Intelligence on communication networks and services

,78 -2851$/ ,&7 'LVFRYHULHV 9RO 0DUFK

,Q UHIHUHQFH WR WKH DERYH GLVFXVVLRQV OHW XV DVVXPH WKH $V VKRZQ LQ )LJ OHW XV FRQVLGHU D VFHQDULR LQ ZKLFK
IROORZLQJ D 7UDQVPLWWHU 7[ DW SRVLWLRQ 3 DQG D 5HFHLYHU 5[ DW
‡ 7KHUH LV D QHWZRUN XQGHU FRQVLGHUDWLRQ SRVLWLRQ 5 DUH VHSDUDWHG E\ D GLVWDQFH µ'¶ DQG WKHUH
‡ WKHUH DUH µX¶ XVHUV VXEVFULEHUV LQ WKH QHWZRUN H[LVWV D SRLQW 4 EHWZHHQ 3 DQG 5 VXFK WKDW 34 LV D IUHH
‡ WKHUH DUH µV¶ VLWHV LQ WKH QHWZRUN VSDFH 7KHQ WR WKH )ULLV 0RGHO WKH WUDQVPLW DQG
WK
WK
‡ WKH µM ¶ XVHU LV VHUYHG E\ µN ¶ VLWH UHFHLYH VLJQDO SRZHU UHODWLRQ FDQ EH H[SUHVVHG E\ > @
‡ WKH XVHUV KDYH LQVWDQWDQHRXV FDSDFLW\ GHPDQG RU
WKURXJKSXW GHPDQG
‡ WKH FDSDFLW\ GHPDQG IXQFWLRQ LQ WHUPV RI ELWV SHU
WK
VHFRQG RI M XVHU LV GHILQHG DV EM W
‡ DOO XVHUV DUH G\QDPLF LQ SRVLWLRQ DQG WLPH :KHUH
‡ WKH YHORFLW\ DQG SRVLWLRQ RI MWK XVHU DW DQ\ WLPH µW¶ ‡ 3W LV WKH WUDQVPLW SRZHU RI WKH QHWZRUN VLWH
LV GHILQHG DV YM W DQG SM W ZKLFK LV WKH YHORFLW\ ‡ 3U LV WKH UHFHLYH VLJQDO SRZHU DW 4 E\ WKH UHFHLYHU
DQG SRVLWLRQ IXQFWLRQ RI XVHU µM¶ ‡ *W LV WKH WUDQVPLW DQWHQQD JDLQ
WK
/HW LW EH DVVXPHG WKDW WKH M XVHU ZDV WKH RQH VWD\LQJ ‡ *U LV WKH UHFHLYHU DQWHQQD JDLQ
DW SRLQW µ3¶ GHFLGHV WR PRYH ZLWKLQ WKH QHWZRUN WR ‡ Ȝ LV WKH ZDYHOHQJWK RI WKH FDUULHU LQ XVH
UHDFK SRLQW µ4¶ ,Q WKLV FDVH ZKHUHYHU WKH XVHU M LV ‡ ' LV WKH GLVWDQFH EHWZHHQ 3 DQG 4
PRYLQJ LW LV UDLVLQJ DQ DGGLWLRQDO GHPDQG DW WKH &RQVLGHULQJ WKH DQWHQQD JDLQV DV XQLW\ WKDW LV
ORFDWLRQ 7KHQ DOO WKH SUREOHPV WKDW ZHUH RQFH *W *U HTXDWLRQ \LHOGV IUHH VSDFH 3DWK /RVV
DVVRFLDWHG ZLWK SRLQW 3 DUH QRZ SURJUHVVLQJ WR SRLQW 4 0RGHO 3/0 JLYHQ DV > @
(DFK WLPH D SHUVRQ RU JURXS RI SHRSOH PRYH WR D QHZ
SODFH DQ DGGLWLRQDO UHVRXUFH GHPDQG LV FUHDWHG ZKLFK
NHHSV RQ VKLIWLQJ IURP SRLQW WR SRLQW DV WKH SHUVRQ RU
JURXS PRYHV 7KXV WKH ORFXV RI WKH SDWK WKDW D SHUVRQ
RU JURXS PRYHV FUHDWHV D GHPDQG FXUYH LQ WKH QHWZRUN 7KH GHFLEHO IRUPDW RI HTXDWLRQ FDQ EH REWDLQHG DV
DUHD
3LFWXUHV LQ )LJ VKRZ WKDW WKHUH FDQ EH µtriggers¶ PL D ORJ PL D RU
VXFK DV PXVLF FRQFHUWV FDUQLYDOV PDUNHW VDOH HWF WKDW fsdB fs
FRPSHO RU PRWLYDWH XVHUV WR DFFXPXODWH DQG PRYH LQ
JURXSV DW XQSUHFHGHQWHG ORFDWLRQV DQG DW XQIRUHVHHQ
WLPHV 7KH PRUH SRSXODWHG WKH $R, LV WKH PRUH FKDQFHV 7KH SDWK ORVV H[SHULHQFHG DW SRLQW 5 DW D GLVWDQFH '
WKHUH DUH RI VXFK UDQGRP ZREEOHV RI DFFXPXODWLRQV IURP 3 FDQ EH REWDLQHG LQ UHODWLRQ WR WKH IUHH VSDFH
7KHVH XQFHUWDLQWLHV JLYH ULVH WR GXELRXVQHVV LQ FDSDFLW\ SDWK ORVV DW D XVLQJ WKH ZHOO NQRZQ SDWK ORVV HTXDWLRQ
DQG FRYHUDJH RI D QHWZRUN GLVFXVVHG EHORZ > @ PHQWLRQHG EHORZ DV

3.3. Place Time Coverage

$V ZH FDQ VHH IURP HTXDWLRQ WKH UHFHLYHG VLJQDO
VWUHQJWK DW D FHUWDLQ GLVWDQFH µG¶ IURP 7[ LV SULPDULO\
LQIOXHQFHG E\ WKH SDWK ORVV H[SRQHQW µQ¶
1RZ OHW XV DVVXPH WKDW D SHUVRQ IURP VRPHZKHUH
UHDFKHV SRLQW 3 DQG VWDQGV EHWZHHQ 7[ DQG 5[ SDWK VHH
)LJ ,Q VXFK D FDVH WKH SDWK ORVV ZLOO QRW EH WKH VDPH
DV ZKDW LV JLYHQ LQ HTXDWLRQ /LNHZLVH LI PRUH SHRSOH
VXUURXQG 5[ WKHUH ZLOO EH VXEVHTXHQW GURSV LQ WKH
UHFHLYH VLJQDO YDOXH ,I DQ 163 GHFLGHV WR GHSOR\ D
PRELOH :&1 XVLQJ VWDQGDUG SDWK ORVV PRGHOV WKHQ WKH
GHSOR\HG QHWZRUN RXJKW WR IDLO LQ VXFK FRQGLWLRQV
7KH QHZ YDOXH RI 3/( FDQ EH H[SUHVVHG DV
n var = n + N AR

)LJ 3ODFH WLPH FRYHUDJH G\QDPLF SDWK ORVV PRGHO

‹ ,QWHUQDWLRQDO 7HOHFRPPXQLFDWLRQ 8QLRQ