client connections share load 50:50 to two websites.

if you want to share information among connections, you may consider using "table" command.

The table Command: Basics by spark

another tricky way is to use global static variable since each tmm has its own value.

my big-ip has 2 tmm. "bar" is front-end virtual server. "one" and "two" are back-end virtual servers. users always connect to "bar" virtual server.

// config

root@(ve13a)(cfg-sync In Sync)(Active)(/Common)(tmos) list ltm virtual
ltm virtual bar {
    destination 172.28.24.10:80
    ip-protocol tcp
    mask 255.255.255.255
    profiles {
        http { }
        tcp { }
    }
    rules {
        qux
    }
    source 0.0.0.0/0
    translate-address enabled
    translate-port enabled
    vs-index 10
}
ltm virtual one {
    destination 0.0.0.0:80
    ip-protocol tcp
    mask any
    profiles {
        http { }
        tcp { }
    }
    rules {
        three
    }
    source 0.0.0.0/0
    translate-address disabled
    translate-port disabled
    vlans-enabled
    vs-index 8
}
ltm virtual two {
    destination 0.0.0.0:8080
    ip-protocol tcp
    mask any
    profiles {
        http { }
        tcp { }
    }
    rules {
        three
    }
    source 0.0.0.0/0
    translate-address disabled
    translate-port enabled
    vlans-enabled
    vs-index 9
}

root@(ve13a)(cfg-sync In Sync)(Active)(/Common)(tmos) list ltm rule qux
ltm rule qux {
when RULE_INIT {
  set static::rr 0
}
when HTTP_REQUEST {
  if { $static::rr } {
    set dest "one"
  } else {
    set dest "two"
  }
  log local0. "s[TMM::cmp_group]/tmm[TMM::cmp_unit]\
    client=[IP::client_addr]:[TCP::client_port]\
    destination=$dest\
    rr=$static::rr"
  set static::rr [expr {($static::rr + 1) % 2}]
  virtual $dest
}
}

// test

 ab -n 10 http://172.28.24.10/

// log

[root@ve13a:Active:In Sync] config  grep tmm0 /var/log/ltm
Dec 31 11:53:38 ve13a info tmm[17969]: Rule /Common/qux : s0/tmm0 client=172.28.72.16:34772 destination=one rr=1
Dec 31 11:53:38 ve13a info tmm[17969]: Rule /Common/qux : s0/tmm0 client=172.28.72.16:34774 destination=two rr=0
Dec 31 11:53:38 ve13a info tmm[17969]: Rule /Common/qux : s0/tmm0 client=172.28.72.16:34776 destination=one rr=1
Dec 31 11:53:38 ve13a info tmm[17969]: Rule /Common/qux : s0/tmm0 client=172.28.72.16:34778 destination=two rr=0
Dec 31 11:53:38 ve13a info tmm[17969]: Rule /Common/qux : s0/tmm0 client=172.28.72.16:34781 destination=one rr=1

[root@ve13a:Active:In Sync] config  grep tmm1 /var/log/ltm
Dec 31 11:53:38 ve13a info tmm1[17969]: Rule /Common/qux : s0/tmm1 client=172.28.72.16:34773 destination=one rr=1
Dec 31 11:53:38 ve13a info tmm1[17969]: Rule /Common/qux : s0/tmm1 client=172.28.72.16:34775 destination=two rr=0
Dec 31 11:53:38 ve13a info tmm1[17969]: Rule /Common/qux : s0/tmm1 client=172.28.72.16:34777 destination=one rr=1
Dec 31 11:53:38 ve13a info tmm1[17969]: Rule /Common/qux : s0/tmm1 client=172.28.72.16:34779 destination=two rr=0
Dec 31 11:53:38 ve13a info tmm1[17969]: Rule /Common/qux : s0/tmm1 client=172.28.72.16:34780 destination=one rr=1