So far the thesis has concentrated on the assumption that to provide an acceptable grade of service the average network blocking should not exceed 0.5% (as it currently is for telephony based services). However, for future, and as yet unforeseen multimedia services, the acceptable grade of service is unknown. It is necessary to understand the performance of the network when the average network blocking is greater than 0.5%.
In Figure 8.5(A) the gradient of the blocking curve for a network without wavelength reuse has been superimposed on the blocking curve of a network with wavelength
reuse. Notice how, once blocking occurs, the curve of a network not employing
reuse techniques rises more steeply that of a wavelength reuse network, which has a more gradual rise (this phenomena was also raised in the previous section) i.e. once blocking occurs (more specifically once it is above 0.5%) the gradient of the network
not employing wavelength reuse techniques is approximately 2 .6 times steeper than
the network employing wavelength reuse.
The reasoning behind this behaviour can be explained by examining the effect which blocking has on the average distance (number of hops) of successfully estabhshed connections. This is shown in Figure 8.21 for a 24 node wavelength reuse network
with the shortest available routing algorithm.
The red curve indicates an offered traffic loading of 245.76 Erlangs; which is the point at which the average network blocking is just greater than 0.5%. At low traffic loads (less than 245 Erlangs) and hence low average blockings (< 0.005) the successfully established calls all traverse a distance of between 0 to 13 hops with the most frequent being between 0 to 11 hops (as expected for a 24 node network). The
average number of hops is 6 as expected. In other words, when the average blocking
is negligible all the calls are routed along their shortest, most direct, route. However, once blocking increases (the red curve represents the point at which blocking exceeds 0.5%), a few of the longer hop calls (between 9 to 11 hops) start being blocked along
Traffic Loading m 491.52 m 423.72 384.00 □ 341.33 □ 299.71 □ 273.06 ■ 245.76 ■ 223.42 189.05 m 160.00 Number of Hops (^J <^J <\j <nj 273.06 491.52 / ' : Increased Traffic voading
Figure 8.21 Relative Number Of Hops By Successfully Established Connections Versus The Offered Traffic
(N = 24 ,Shortest Available Algorithm, 100 Wavelength Pairs)
calls are routed around the ring via the alternative longer route. Hence, when blocking first occur the range of distances traversed by calls becomes larger (to around 16 hops for a traffic loading of 341 Erlangs). However, notice how the curves starts to peak towards the shorter hop calls; as the traffic loading continues to increase, the likelihood of finding a long continuous length of unused wavelength becomes less and less likely. So as traffic on the network increases, the call requests which require routes spanning several hops (4 to 11) become more likely to be blocked than those calls which span only a few hops (0 to 4). Figure 8.21 shows these effects clearly, as the traffic increases and the average blocking of the network increases, the curves gradually tend to peak towards the shorter hop calls.
One would expect, taking this argument further, that as the average network blocking approached one, the majority of connections requests which are successfully established would be those which originate and terminate on the same PON (requiring only one hop) and hence the maximum number of connections which could be simultaneously established is equal to the number of nodes multiplied by the number of wavelength pairs (A^xW).
In actual effect, a call routed around the ring which travels a distance of H hops can
be considered to be using as much capacity as H calls traversing a distance of 1 hop
would. Once blocking occurs, establishing a connection over a distance of H hops
could, in the worst case scenario, be causing -1) caUs to fail at a later time because
they are no wavelength pairs available.
If this is the case, then the shortest available routing algorithm is only useful as long as the maximum acceptable grade of service dictates the need for the blocking to always be below 0.5%. Once blocking approaches 0.5%, routing a call around the long way around the ring could cause the several future connection requests to be
refused. This confirms, once again, the results obtained in section 8.3.2 (Figure
8.12). But it has already been shown that the shortest acceptable routing algorithm performs better than the shortest only routing algorithm at low blocking. However, as the offered traffic increases and the network becomes busier and busier, this technique of routing uses a lot of capacity for a small increase in the network throughput. Can the shortest available routing algorithm be improved upon to overcome the issues raised in the previous paragraph?
What is required is a routing algorithm which
(i) takes into consideration the difference in distance (no of hops) between the shortest and the alternative route
(ii) takes into consideration the capacity remaining on the intermediate nodes transversed in order to establish up the connection
(iii) penalises the use of a route if the capacity it uses is too great (the size of this capacity needs to be dependent on the difference between the distance of the shortest and the alternative longer route).
8.7 RESERVATION ROUTING (RR) ALGORITHM
In the reservation algorithm, choosing the route between source and destination users is dependent on the hop distance between the source and destination users, the average blocking of the network at the time the connection request is received and the unused remaining capacity on the intermediate nodes on the routes between the two users.
Assuming a continuous wavelength pair can be found on both the shortest and the alternative route, the shortest and most direct route is chosen only if the following equation does not hold true
where R is the reservation parameter, is number of hops between the users if
the alternative route is used, whilst Lgg is the length of the shortest route. CA^i„ is
the Minimum Capacity of the intermediate node on the Alternative Route and
the Minimum Capacity on an intermediate node on the Shortest Route. The Offset is included in the simulation to provide flexibility within the program should any fine tuning be required during run time. Initially the offset was taken to be zero.
If the equation holds true the call is routed along the longer alternative route otherwise the shortest most direct route is used.
The above RR scheme described is similar to a reservation scheme recommended by
Frank Kelly and Richard Gibben[107] which was applied to the long haul trunk network using circuit switching techniques. Their algorithm was applicable to a fully meshed architectures in which several possible routes between node pairs existed. Kelly and Gibbens proposed an algorithm which always attempted to establish a
connection between a node pair along the most direct (1 hop) route first (in a similar
manner to the SR algorithm described earlier). If the shortest direct route failed (due
to congestion or other reasons) all the alternative routes which required only two hops were considered in turn. In order to maximise the network throughput without adversely effecting future connection requests, they penalised the two link calls when
the alternative routes were busy. The method of achieving this was to define a trunk-
reservation parameter k . The alternative "two hop route could only be used to route information between a node pair if there were at least k free lines on each of the two links." If, on the other hand there are fewer than k free lines on either of the two links the connection request is barred from using that route.
Perhaps surprisingly, they found that the performance was very insensitive to the
exact value of k. So long as k was not equal to zero the system performed well. For
links of a few score up to many thousands of lines, taking k anywhere between 5 and
10 performed acceptably. This techniques has been patented under the well known
Dynamic Routing Algorithm (DAR) name. For more information on simulation
studies of Dynamic Alternative Routing Schemes the reader is referred to [107] [108].
The reservation routing scheme used in the LambdaPON network differs from the trunk reservation scheme proposed by Kelly. The more noticeable of these differences are
(ii) at present the Lam bdaPON netw ork studied have not been fully m eshed (although the wavelength reuse principle is just as applicable to fully meshed LambdaPONs) and hence it is not possible to simply limit the establishment of a
connection to a maximum of 2 hops.
(iii) defining the reservation param eter is not as straight forward; the reservation param eter needs to be dependent on the number of hops required to establish the connection request on the alternative routes.
The use o f the RR scheme should yield an im provem ent in the Lam bdaPO N
throughput. The RR algorithm has been tested and simulated. Results from the
simulation are shown in Figure 8.22 and 8.23.
eg js 2 Ou UD C _o CQ OJD eg k V > < ().()0()15 ().()()() 14 ().()()() 13 ().(KK)12 ().(HK)11 ().(KX)1() ().()( )009 ().()( )()()8 O.OOOO? ().0(K)()6 ().()()()()5 ().()()()04 ().()()(K)3 □ ---1 1 1—1—!—1— 24 Nodes 1--- 1 ▼ T < mcm: IS 1I
in^1Nietv or Vit)\iSAÏ : AIgoritim
R 11 ■^11 u I!□ n SB 1 1 1 □ 1 ta CN TT OO o o d d r—' ^ o i <N CN cm’ ( r i f r i Value Applied to R
Figure 8.22 The Variation Of the Average Network Blocking with R
The value applied to R is found to greatly effect the perform ance o f the RR
Algorithm. So long as the value applied to R is between 2 and 3, for a 24 node bi
directional ring, the algorithm is found to perform better than either the SAR or SR algorithms by approximately an extra 1.8 Erlangs of offered traffic at 0.5% blocking, a very m arginal im provement. A com parison o f the perform ance of the various algorithm s is show n in Figure 8.23. Once again, as with the SAR versus SR
algorithms, the im provement in performance of the RR is primarily at low blockings.
Note that the value of the reservation parameter R is very sensitive in the case of the
LambdaPON network unlike the value of k..
.o eg 2 On ex s % & eg u > < 0.010 0.009 0.008 0.007 0.006 0.(05 0 .0 04 : 0.003 0.002 0.001 0.000
^ Shortest Routing Algorithm ^ Shortest Available Algorithm
Reservation Routing Algorithm
180 200 220 240 260
Average Total Traffic Offered (Erlangs)
Figure 8.23 Comparing the Performance Of The Different Routing Algorithms
Figure 8.24 com pares the effects of the RR and the SAR algorithm on the number of hops traversed by successfully established connections. Interestingly, w hilst the blocking probability of the RR is lower than that of the SAR algorithm for 204.8 Erlangs of offered traffic, the hop curves for the Reservation Algorithm are similar to those expected for the SAR algorithm when blocking occurs (compare with Figure 8.21). The reason the curve for the RR curve appears like this is because for connection requests with hops between 9 and 11, the RR algorithm autom atically routes these calls around the ring using the longer route, if the capacity along the longer route is greater than that along the shorter route and equation 7.1 does not hold
true. T his, how ever, results in a w orse perform ance at higher traffic loads,
I
r 0> > ••n CQ I 9 Ring (SAR) 8 R = 2.2 7 R = 2 .6 6 R = 3 .5 5 4 3 2 0 CO Number of HopsFigure 8.24 The Effect of The Reservation Algorithm On The Average Number
of Hops Traversed. (Offered Loading equal 204.8 Erlangs)
Referring to sections 8.6 and 8.7, one striking feature of the LambdaPON network is
that once blocking occurs it is the longer hop calls which
(i) are blocked most and
(ii) use up more network capacity and hence could cause a larger number of calls
to be blocked in the future.
Therefore, one obvious method which could be used to increase the network throughput would be to have an algorithm which, once blocking starts to occur, simply refuses to connect calls requests which need to be routed over a certain
maximum number of permissible hops, //max- The value of Hmax needs to be
dependent on the average blocking of the network. This type of algorithm (the "unsocial policy algorithm") would be more in line with Kelly’s trunk reservation algorithm.
However, whilst this type of algorithm might be suitable for the trunk network it would not be suitable for use in the access network. In the access networks the establishment of connection requests is on a per-call-basis and occurs frequently; unlike connection requests in the core network, in which the establishment of new connections between node pair might only be once a day or even week. Additionally in the trunk network, the establishment of a route between two nodes is used to
transport traffic from a large number of traffic sources (users). The unsocial policy
algorithm is unfair to those calls which span a large number of hops. This bias against long call hops is, once blocking occurs, unsuitable because it deteriorates the grade of service for users making long hops.
8.8 FACTORS EFFECTING THE THROUGHPUT PERFORMANCE OF
THE LAMBDAPON
From the results obtained so far it appears that the throughput of the LambdaPON is detrimentally effected primarily by
(i) the long hop calls which utilise a lot of the network's capacity.
(ii) fragmentation of the wavelengths which is wasteful of the available network
capacity and hinders the number of times a wavelength can be reused.
To overcome the effect mentioned in (i), the reservation algorithm was found to provide an improvement. However, the improvement was found to be relatively small and the complexity in applying an algorithm (such as that described) is relatively complicated because of the need for the value of R to be dynamically controlled according to offered traffic load.
A simpler method of reducing the average distance traversed by calls is to alter the topology of the network, i.e. to provide a greater degree of meshing. By increasing the number of routes between the nodes, the average number of hops should be reduced thereby increasing the degree of wavelength reuse achievable. The effect of varying the physical topology is studied in depth in section 8.9.
To reduce the fragmentation of the wavelengths (ii) several techniques can be applied;
(a) alter the wavelength allocation algorithm to minimise the degree of
fragmentation (studied in section 8.10)
(b) utilise wavelength translation in order to remove the constraint of wavelength continuity and thereby increase the probability of finding an unused wavelength (section 8.11)
(c) redesign the network protocols and replace the tunable receivers and
transmitters by ultra-fast tunable receivers and transmitters which are capable of being tuned in mid-call without the call being dropped. This method allows the reassignment of wavelengths to calls whilst they are in session and hence assists in the optimisation of the wavelength packing. This technique is likely to be very processor intensive and the ability to apply it to a network will be strongly
dependent on the availability of the ultra-fast tunable receivers and transmitters; hence it is dealt with separately in Chapter 10.
8.9 VARYING THE PHYSICAL NETWORK TOPOLOGY
There are far too many possible network configuration which could be studied and it is necessary to hmit the type and number of topologies which are studied. The aim in this section is to study a few different topologies to gain an insight into the effect of varying the network topology and to obtain a general pattern which should be applicable to other types of networks topologies.
The network studied have are based on bi-directional rings with various degrees of additional meshing. The meshed rings have been limited to the consideration of only symmetric network topologies since the traffic distribution has, up to now, been symmetric. If the offered traffic were non-symmetrical then non-symmetrical topologies would need to be considered. For simplicity, the topologies studied can be perceived as being a bicycle wheel, i.e. a bi-directional fibre ring (similar to a bicycle rim) with a varying number of spokes attached in such a manner that the wheel is always symmetric.
8.9.1 Meshing With Links Spanning NH Nodes
Consider the simplest alternative topology based on the ring; in other words an N node bi-directional ring with 1 additional link such as that shown in Figure 8.25 (A). One expects that by adding the additional link between nodes 1 and 13, as shown, the throughput of the network should increase because the average number of hops per connection request should be lower than that of the simple bi-directional ring topology. For example, calls between nodes 1 and 12 which would originally have been routed via the route 1—>2 -^3 —>...11—>12, and hence used up a total capacity of 11 at the nodes, can now instead be routed along the route 1—> 13 —>12 and use a capacity of only 3. This allows the same wavelength to be allocated to another call anywhere along the route 2 - ^ 3 —>... 10 ^ 11.
However, closer examination of the network reveals that the expected increase in throughput might be not be so straight forward. Any connection requests between users on the green nodes to users on the red nodes (and vice versa) will first attempt to find a route using the central link between nodes 1 and 13. This is also true for connections between nodes 4 and any of the red nodes, 10 and any of the green nodes, 16 and any of the green nodes, and finally 22 and any of the red nodes. Hence,
establish the shortest route between a large set of node pairs. As the traffic on the netw ork increases, the capacity on nodes 1 and 13 gets quickly used up until eventually, there is no more capacity on nodes 1 and 13 even though capacity exists on the other nodes between nodes. Once this occurs the ring effectively becomes split into two, and users on one half of the ring (X+) can no longer contact users on the other half of the ring (X-) and vice versa. This is shown clearly in Figure 8.25(B). Since calls can no longer cross the boundary form ed by the nodes 1 and 13, the perform ance of the network deteriorates rapidly. Hence, placing an additional link
across the bi-directional ring should result in a reduced network throughput rather
than an improvement as hoped.
(A) (B)
Figure 8.25 A Bi-directional Symmetrical Ring With 1 Additional Link This above effect is primarily a function of the method used hy the routing algorithm to define the shortest path between node pairs. At present the shortest route routing