Performance Analysis of Dijkstra-Based Weighted Sum Minimization Routing Algorithm for Wireless Mesh Networks

Algorithm 1

The Dijkstra-based routing algorithm (optimizing path capacity).

(1)  INPUT: no. of nodes 𝑛, source node 𝑣𝑠, destination node 𝑣𝑑, 𝑟(𝑙) for all 𝑙.

(2)  OUTPUT: 𝑃^∗(𝑣𝑠,𝑣𝑑),𝑅(𝑃^∗(𝑣𝑠,𝑣𝑑))

(3) /* Initialization */

(4)  FOR ALL nodes

(5)   Incorporated nodes = NIL

(6)   𝑅(𝑃(𝑣𝑠,𝑛𝑜𝑑𝑒))=0

(7)   Parent(node) = NIL

(8)  END

(9)  𝑅(𝑃(𝑣𝑠,𝑣𝑠))=∞

(10) FOR  𝑖=1∶(𝑛−1)

(11)   FOR ALL incorporated nodes

(12)     𝑅𝑎𝑡𝑒(𝑛𝑜𝑑𝑒)=𝑅(𝑃(𝑣𝑠,𝑛𝑜𝑑𝑒))

(13)   END

(14)   𝑟_max=max[𝑟𝑎𝑡𝑒(𝑛𝑜𝑑𝑒)]

(15)   𝑢 = node corresponding to 𝑟_max.

(16)   /*  𝑢 is the incorporated node  */

(17)   FOR ALL nodes 𝑣

(18)     IF  𝑟(𝑙_𝑢𝑣)<𝑅(𝑃(𝑣𝑠,𝑢))  THEN

(19)      𝑐𝑎𝑝=𝑟(𝑙_𝑢𝑣)

(20)     ELSE  𝑐𝑎𝑝=𝑅(𝑃(𝑣𝑠,𝑢))

(21)     END IF

(22)     IF  𝑐𝑎𝑝>𝑅(𝑃(𝑣𝑠,𝑣))  THEN

(23)      𝑅(𝑃(𝑣𝑠,𝑣))=𝑐𝑎𝑝

(24)      𝑝𝑎𝑟𝑒𝑛𝑡(𝑣)=𝑢

(25)      /*  𝑃(𝑣𝑠,𝑣)=𝑃(𝑣𝑠,𝑢)⨁𝑙_𝑢𝑣  */

(26)     END IF

(27)    END FOR

(28)    IF  𝑝𝑎𝑟𝑒𝑛𝑡(𝑣𝑑)≠ NIL THEN

(29)     𝑃(𝑣𝑠,𝑣𝑑)=[𝑣𝑑]

(30)     𝑡=𝑣𝑑

(31)     WHILE  𝑡≠𝑣𝑠

(32)        𝑝=𝑝𝑎𝑟𝑒𝑛𝑡(𝑡)

(33)        𝑃(𝑣𝑠,𝑣𝑑)=[𝑝𝑃(𝑣𝑠,𝑣𝑑)]

(34)        𝑡=𝑝

(35)     END

(36)    END IF

(37) END FOR

(38) 𝑃^∗(𝑣𝑠,𝑣𝑑)=𝑃(𝑣𝑠,𝑣𝑑)

(39) RETURN  𝑃^∗(𝑣𝑠,𝑣𝑑),𝑅(𝑃^∗(𝑣𝑠,𝑣𝑑))