CHAPTER 5. Survivable Network Design
5.2 Dynamic Survivable Network Design
In this section, we develop a solution for survivable network design in the presence of dynamic traffic. In [83], three approaches for shared protection in the context of dynamic traffic in LP-TG networks were proposed - protection at the lightpath level, mixed protection at the connection level and separate protection at connection level. The trade-offs made between transceiver usage and wavelength usage were analyzed and the authors conclude that protection at the connection level performs better than protection at the circuit level for lightpath based networks. Two approaches for dedicated protection in LP-TG architecture were proposed and evaluated in [84].
In the discussion that follows, we first introduce the motivation of the design problem. Next, we present some of the assumptions made in our work, the constraints related to the problem, the objective we want to accomplish and a description of the algorithm we implement followed by a discussion on the simulation results we obtained.
5.2.1 Problem Motivation
In this section, we design a solution for mixed shared protection in the presence of dynamic traffic for mesh networks that aggregate traffic at the path level. There have been numerous initiatives in the literature for developing algorithms for protection in the context of LP net- works that have clients with e-grooming capabilities [84, 83, 133]. However, our current work is focused on all-optical networks.
Consider the following assumptions for an example six node LT network shown in Figure 5.4 for illustration purposes. Let the capacity of a wavelength be 5 units and size of individual requests be 1 unit. There is one wavelength per link and there is no restriction on the number of transceivers per node. Initially, there are no calls in the network and no wavelengths and transceivers are used. Let the call arrivals be (1, 4), (1, 6), (5, 4) and (6, 5), in that order and calls are to be routed in a survivable manner, with the requirement that the primary take the shorter path than the secondary. Let T =< ti : i = 1..6 > and R =< ti : i = 1..6 >, where
ti and ri denote the number of transmitters and receivers used at node i respectively to carry
the specified requests. Let Re(Ci) be the residual capacity of circuit Ci.
Consider the first call (1,4). The primary is routed along the link 1-4 through circuit C1.
The secondary is routed along the path 1-6-5-4 through circuit C2. The status of the network
is T =< 2, 0, 0, 0, 0, 0 >, R =< 0, 0, 0, 2, 0, 0 > and Re(C2) = 4. When the next call (1,6)
arrives, the primary can be routed along circuit C2 and the secondary is routed along 1-2-6
to create circuit C3. The new network status is T =< 3, 0, 0, 0, 0, 0 >, R =< 0, 0, 0, 2, 0, 2 >
and Re(C2) = 4. Note that the connection can be accommodated without addition of a
new transmitter at node 1 and that the residual capacity of C2 remains the same since the
call is accepted, T =< 3, 0, 0, 0, 2, 0 >, R =< 0, 0, 0, 3, 0, 2 > and Re(C2) = 3. When the last
call (6,5) arrives, the network state becomes, T =< 3, 0, 0, 0, 2, 2 >, R =< 0, 0, 0, 3, 2, 2 > and Re(C2) = 2. If the circuits used were SLT, the third and fourth calls would be dropped. If it
were DLT, the second and fourth call would be dropped and if it were LP, the first call alone is accepted.
It is clear that different networks lead to different blocking performance. We would like to design an algorithm that can perform survivable network design for all the different ar- chitectures and yield results that can be used to quantify their comparative performance. In the past, an ILP formulation for static LT network design was proposed for rings in [53]. An ILP formulation was provided for shared protection in LT mesh networks in [56]. An ILP formulation and heuristic for dedicated protection was provided for LT mesh in [4]. However, to the best of our knowledge, shared protection in the presence of dynamic traffic for LT mesh networks has not been investigated before. Though we develop the algorithm for LT, we note that it is applicable for all the other path based aggregation strategies through simple changes in the virtual topology representation. This allows us to use the approach to compare the performance of the various path based strategies.
5.2.2 Assumptions
• The physical topology is given by G = (V,E), where V is the set of nodes and E is the set of fiber links connecting the nodes.
• The capacity of each wavelength is arbitrarily assigned to be C = 10, the number of wavelengths on each link is W and the number of transceivers on each node is X. The transceivers are tunable to any wavelength in the fiber.
• The call arrivals to a network are assumed to be poisson distributed and the call depar- tures are assumed to be exponentially distributed with a rate normalized to unity. • The calls are uniformly distributed between arbitrary source destination pairs.
Input : G(V, E), < s, d, B, th >, Co(e), C, φte and all other information for every circuit t,
wavelength state and transceiver state, where s - source, d - destination, th - holding time, B -
connection bandwidth, Co(e) - cost of edge e, and C - capacity of a wavelength.
Output: Link disjoint working and backup circuit.
STEP 1: Compute the auxiliary graph based on the wavelength state, transceiver state and existing circuit information.
STEP 2: Prune edges that cannot handle the request capacity B. Compute minimal cost path from the output vertex of the access layer on node s to the input vertex of the access layer on node d to be pw.
STEP 3: If primary is not routable, drop the call. Otherwise, proceed to the next step.
STEP 4: Compute minimal cost path pb from the output vertex of the access layer on node s to the
input vertex of the access layer on node d by assigning a new cost C0(e) to every edge e as follows:
a. if edge e does not represent a link or a circuit, C0(e) = Co(e)
b. if edge e represents a link, C0(e) is
– +∞ if e is not route disjoint with pwor link does not have a free wavelength
– BCo(e) otherwise
c. if edge e represents a circuit k, C0(e) is
– +∞ if circuit k is not route disjoint with pwor (φ∗t − φ
e0
t ) plus the residual capacity of
k is less than B for some edge e0 traversed by pw
– if circuit k is route disjoint with pwand (φ∗t− φe 0
t ) plus the residual capacity of k is no
less than B for some edge e0 traversed by pw
– B0C
o(e) otherwise, where B0 = B − min{φ∗t − φe
0
t } for every edge e0 traversed by pw
STEP 5: If secondary is not routable, drop call. Otherwise, proceed to the next step.
STEP 6. Update network state and circuit information corresponding to backup route pb. For every
link e traversed by pw, φet = φet + B. Compute the new value of φ∗t. If required, remove wavelength
links and add/modify edges in the virtual topology layer.
• The call sizes are sub wavelength in nature and individual granularities have equal ca- pacity arrival rates.
5.2.3 Constraints
Wavelength Continuity Constraints: We assume that wavelength conversion is not present in the network. So, there is a requirement for a wavelength continuous route from source to destination.
Resource Constraints: The number of wavelengths per link and number of transceivers per node are limited and pre provisioned.
Diverse Routing Constraints: The primary path should be link wise disjoint from the secondary path.
Circuit Capacity Constraints: A wavelength in a network consists of the following four dynamic partitions:
• Primary capacity
• Dedicated backup capacity • Shared backup capacity • Residual capacity
The sum of the sizes of these partitions should add up to the capacity of a wavelength.
5.2.4 Objective
The objective is to minimize blocking performance and identify a path disjoint backup route for every primary route. This can be achieved by maximizing backup bandwidth sharing without violating capacity constraints.
5.2.5 Algorithm
In our current work, we exploit the concept of backup sharing to minimize blocking perfor- mance. Shared backup leads to capacity savings at the expense of reduced restoration speeds
and can be explained as follows. Assume a circuit t of capacity 10 units packed with 6 units of primary traffic. The 4 units spare capacity can carry a backup connection c of size 4 units if c is in the backup containment set of t. This spare capacity can also be shared as well. If two backup connections of size 4 units each conform to the backup containment set of t, then both could share the 4 units spare capacity on t, if their corresponding primaries will not fail together. To keep track of the shared backup capacity, the following information is maintained for every trail t:
• The route, the wavelength assignment and the residual capacity of trail t • For every link e, φe
t identifies the amount of traffic to be routed over the trail t if link e
fails. • φ∗
t refers to the maximum value of φte for all e in the network.
The parameter φe
t captures information related to backup sharing. φ∗t is the amount of backup
capacity reserved on circuit t. The value of (φ∗
t-φet) refers to the amount of free bandwidth
available on circuit t for backing up a connection that traverses link e. Using this free bandwidth available on circuits and the residual capacity on links and circuits, the backups are routed so as to minimize the used extra capacity. The details of our algorithm are provided in Figure 5.5 and described below.
When a call arrives between source s and destination d, we compute the auxiliary graph based on information related to existing circuits, wavelength and transceiver state, cost of the edges and the backup sharing information φet for every edge e. Based on dijkstra’s algorithm,
the shortest route is found from the output port of the access layer of node s to the input port of the access layer of node d. If the primary is not routable, the call is dropped. The transceiver and wavelength status are updated temporarily so as to find the backup route. An edge disjoint backup route from s to d is computed after assigning new cost to all the edges in the network. It is possible to route the backup connection of a call on a circuit edge such that the additional bandwidth consumed is either minimal or zero. The costs of the edges are made proportional to the amount of additional capacity required by the edge to support the
1e-06 1e-05 1e-04 0.001 0.01 15 15.5 16 16.5 17 17.5 18 18.5 19
Capacity Blocking Probability
Transceivers LP SLT DLT LT (a) (b)
Figure 5.6 (a) Throughput as a function of number of transceivers per node for X = 25 and R = 125 E (b) Throughput as a function of W = 23 and R = 50 E
backup connection. By selecting the minimal cost route, the additional bandwidth required to support this connection is minimized at the network level. If there exists no backup route, the call is dropped. Otherwise, the information for backup multiplexing is updated on all the trails that carry the backup connection. The call is accepted and all the required wavelength and circuit information are updated.
5.2.6 Simulation Results
We implemented the dynamic protection model discussed above using discrete event simu- lation techniques. The simulations were performed on random topologies that were generated based on the Waxman model discussed in Chapter 4. The parameters, α = 0.4, and β = 0.3 were used to generate a random two connected mesh network with 20 nodes, 73 links, and a diameter of 5. The simulations were done for both scenarios - transceiver constrained scenario and wavelength constrained scenario. A million calls were generated and capacity blocking performance is reported after a steady state was achieved.
The wavelength constrained scenario is reported in Figure 5.6(a) with X = 25 and Load = 125 Erlangs. The transceiver constrained scenario is reported in Figure 5.6(b) with W =
23 and Load = 50 Erlangs. From both the figures, it is clear that LT performs the best, closely followed by SLT and DLT and LP performs the worst. Naturally, when the transceivers or wavelengths are increased, blocking reduces. There is more than an order of magnitude difference between LT and LP in terms of capacity blocking performance.
5.3 Conclusions
In this chapter, we discussed possible protection mechanisms in light-trail networks, rea- soned why STRAW is a challenging problem and designed heuristics for dedicated and shared connection level segregated protection. We found that, with dedicated protection, about 200 % redundancy may be required. Shared protection performs much better and full protection can be achieved in the presence of single link failures with less than 100 % redundancy. Our current static survivability work considers segregated protection.
We described an auxiliary graph based algorithm for survivable network design with dy- namic traffic. We used this idea to compare the performance of LP, SLT, DLT and LT ar- chitectures. We observed that for random mesh topologies with transceiver and wavelength constrained scenarios, LT performs orders of magnitude better than LP architecture.
Our ILP results for static traffic suggest that optimal solutions involve trails that multi- plex both primary and secondary connections. We would like to design heuristics for mixed protection strategy in the future. We also intend to consider multi-hop scenarios and compare the performance of different architectures.