Descripción del Proyecto Rob and Carla Residences

mal because the amount of future knowledge is limited. Since rerouting is not allowed for existing connections, in practice, the optimization of a sequence of oracular future arrivals is always placed on a residual network with some existing connections. In particular, given information about a number of fu- ture requests (as well as the current state of the network and the termination times for active connections) the oracle selects routes for future requests in a way that minimizes the number of those requests that cannot be routed. This oracular result thus puts a lower bound on the blocking rate achieved by any algorithm operating in the window considered. The oracular window size is selected so as to make the problem of finding the oracular optimum tractable.

I now describe the oracle optimization problem in more detail and present an ILP formulation that allows us to solve it. Optimization begins at a specific simulation time after the network has reached a steady state. In addition to information about the current state of the network and hold time information for all active connections, the optimizer receives a number of future requests with arrival and departure information. (This is the “oracle” part; no real algorithm can have such information.) Figure 4.29 shows an example of six oracle requests and active connection information that should be recorded. (The routes used by each connection active at the start of the optimization window must also be recorded, of course, but are not readily shown by a timeline.)

Let E be the set of graph links, and let R be the set of oracle request pairs, including the arrival and departure timestamps. Let t be a discrete timeline ordered by the arrival time of requests. Therefore, a set of requests sorted by arrival time can be indexed by t. Let rt _{be the request that arrives at time}

t, and let drt be the scheduled departure time for request rt. Let C_e,t be the

residual capacity on link e at time t, at which point any capacity freed by the termination of active connections before time t has been considered in the network resource constraints. Let Prt be the set of all available paths for

request r based on the network’s residual capacity at time t. Let qrt be the

requested capacity of pair rt_{. Let Q}

e represent the set of paths that traverses

edge e _{∈ E. Denote by y}rt a binary variable representing the acceptance

of request rt_{. A solution with r}t _{= 0 implies that r}t _{is not taken, while a}

value of 1 means taken. The variable xrt_,p is a positive integer representing

number represents the number of wavelength channels assigned to that path. The ILP formulation is stated as follows.

Maximize X rt yrtq_rt ∀rt _{∈ R,} X p∈P_rt xrt_,p ≥ y_rtq_rt (4.16) ∀rt_{∈ R, ∀e ∈ E,} X p∈Qe∩Prt xrt_,p+ X rτ_{:τ <t,d} rτ≥t X p∈Qe∩Prτ xrτ_,p≤ C_e,t (4.17) xrt_,p ∈ Z+ (4.18) yrt ∈ {0, 1} (4.19)

Equation (4.16) ensures that for each accepted request (right side), enough paths have been allocated to handle the request (left side). Equation (4.17) constrains the channels utilized at any point t in time and at any edge e to the capacity available in the network. The right side of the equation is simply the capacity available in the link e at time t, considering both the initial capacity of the link and the capacity dedicated to connections that were active at the start of the optimization period and have not yet terminated. The terms on the left side include the channels to be provided for request t, as well as the channels provided for other connections allocated before t and terminating after t. The last two equations constrain the values of the integer variables that specify how requests are accepted and routed. As a general form, the ILP solution may assign multiples to one request that maximize the utilization of network resources. However, I do not consider a request capacity greater than one here; thus, no splitting of capacity would occur on multiple available paths. Equivalently in the ILP formulation, the x variables are binary and qs are uniformly one.

Finally, I compare RFR and CAR with the oracular optimal result (OPT) in Figure 4.30. Due to the limitation of computational resources for larger networks, we reduce the per link capacity to 48. Dynamic arrival rate ranges from 1 to 10. Each request asks for one unit capacity. No splitting of paths

Oracle optimization period

time Starting time

1

End time

Start residual capacity Tailed departures

Updated residual capacity

2 3 4 5 6

History Unknown future

Oracle requests

Figure 4.29: Illustration of Oracle requests.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.8 0.85 Blocking probability Load ratio SPF WSP RFR CAR OPT

Figure 4.30: Comparison of blocking rates on NJ LATA and OPT.

and obtain a steady state. Then, the next 200 requests are routed by SPF, WSP, RFR, and OPT, respectively. Each data point is an average of 1000 experiments. In this experiment, starting with the same initial network state, CAR is the closest online algorithm to OPT. As the network load increases, the gap between RFR and OPT increases, showing that oracular knowledge becomes increasingly important to reduce blocking in congested network states. Without the aid of oracular knowledge, CAR provides the lowest blocking rate.

4.4

Conclusion

I propose a reduced flow online routing algorithm that provides the lowest blocking and network resource usage, compared to commonly used online algorithms. RFR is most robust to changes in traffic load and shows timing advantages relative to other flow-based algorithms. I also improve online routing with threshold-based admission controlled mechanisms. Using an opportunity cost model, I efficiently estimate the optimal threshold value for the threshold. The model enables me to find several improved conges- tion estimation routing algorithms. Compared to other algorithms found in previous studies, CAR-M is fast and the optimal threshold value can be identified analytically and is robust to changes in important network param- eters, such as topology and capacity. I also discuss an oracular optimization model, showing that the long-term optimization of a network is practically impossible. The results show that good performance is achieved more effec- tively through deciding whether to admit an available route altogether versus which route to use.

CHAPTER 5

DIMENSIONING DYNAMIC

TRANSLUCENT NETWORKS

This chapter discusses the problem of dimensioning resources for dynamic translucent networks. In particular, I consider the Reconfigurable Optical Add-Drop Multiplexer (ROADM) network model, which is introduced in Section 2.1.1. For these networks, optical transponders (OTs), 3R regener- ators (REGENs), and wavelengths are disjoint network resources that must be considered separately. A previous study [40] addressed only the REGEN placement problem for this type of network. However, OTs, REGENs, and wavelengths can all affect overall blocking probability, so understanding the dynamics between blocking probability and each resource type is a more im- portant problem. With more variables, dimensioning translucent networks becomes more challenging than dimensioning opaque ones.

I choose CORONET as a targeted design for an efficient resource dimen- sioning algorithm. Poisson dynamic traffic and four different wavelength operating modes with different levels of wavelength channel restrictions are anticipated for the network. I propose a dimensioning algorithm for OTs, REGENs, and wavelengths and evaluate the performance and cost under the four operating modes. My study shows that bounding the upper limit of the set of usable wavelength achieves the most balanced resource usage.