Host autoassignment ipv6 » Historial » Revisió 4
Revisió 3 (Victor Oncins, 22-11-2012 11:01) → Revisió 4/7 (Victor Oncins, 22-11-2012 11:36)
h1. Auto-assignment of IPv6 host-oriented prefixes and collision estimation One of the desired features is qmp nodes are able to offer native IPv6 addressing to final hosts. IPv6 based networks usually assign /64 prefix to each host-oriented interface, subnetted from a bigger /48. This implies the nodes have 2^16 possible /64 prefixes to auto-assign. If we want to use MAC address numbering and grant the non-coincidence of auto-generated prefixes, as a mapping value, we'll need a mapping function from 48 bits of MAC to 48 bits of IPv6 prefix. According to this auto-configure addressing philosophy, we deduce that is impossible to avoid the election of the same prefix /64 (collision) by one or more network interfaces. Thus the collision probability is greater than 0 if more than one network interface is auto-addressed. We Anyway, we could calculate this probability and then estimate the maximum number of network interfaces that can be auto-addresses with a probability collision probability less than certain value. Let l as the last l LSB l-LSB of a MAC address, where 1<=l<=24. We left the first 24 bits from OUI. Thus we have a k=2^l possible endings. If we have in the network N different OUI, OUI we'll have p=N*2^(24-l) possible MAC addresses for each possible ending. Obviously n=k*p is the total space of possible MAC present in that a network. If the network randomly includes two or more MAC with the same l-bit ending, ending from different OUI we'll have a collision, i.e. the same IPv6 /64 prefix will be auto-assigned on different network interfaces. If we select randomly m (m < k) k interfaces (MAC addresses) from N OUI, we obtain n! ------ m! n-m! n!/m!n-m! different combinations without replacement. This set of m MAC addresses will contain a subset of combinations where all its MAC addresses have with different l-bits ending. These combinations will generate /64 prefixes without collision. The number of such combinations with all different ending is k! ------- k!/m!k-m! * p^m m! k-m! thus the non-collision probability is k! n-m! P_nc(m) Pĉ(m) = -- ---- k!/n!*n-m!/k-m! * p ^m n! k-m! p^m If only one interface is present in the network P_nc(1) Pĉ(1) = kp/n = 1, i.e. the collision is impossible. We can now calculate the maximum number M of interfaces such that the probability of collision is was less than certain value. The following table shows this number for a maximum collision probability of 4%. |_.Prefix size |_.l |_.M Prefix l M for N=2 |_.M M for N=20 |_.M M for N=200 | |/51 ---------------------------------------------------- /51 |13 13 |27 27 |27 27 |27| 27 |/50 /50 |14 14 |38 38 |38 38 |38| 38 |/49 /49 |15 15 |53 53 |53 53 |53| 53 |/48 /48 |16 16 |74 74 |74 74 |74| 74 |/47 /47 |17 17 |105 105 |104 104 |104| 104 |/46 /46 |18 18 |148 148 |147 147 |147| 147 |/45 /45 |19 19 |210 210 |208 208 |208| 208 |/44 /44 |20 20 |298 298 |294 294 |294| 294 |/43 /43 |21 21 |428 428 |416 416 |415| 415 |/42 /42 |22 22 |627 627 |520 520 |587| 587 |/41 /41 |23 23 |957 957 |839 839 |830| 830 |/40 /40 |24 24 |1656 1656 |1202 1202 |1174| 1174 We note that the variation of M with the number of OUI is very small. Thus the maximum number of interfaces in a /48 network with a collision probability 4% is 74.