TRUNK RESERVATION ANALYSIS OF TELUS' EDMONTON TELECOMMUNICATION NETWORK

INFOR, Aug 2003 by Sim, Thaddeus

A call connecting on its direct path is termed a direct call (for example, path 1 in Table 1), while a multi-link call is one that connects on one of the multi-link paths of the route (paths 2 and 3 in Table 1). The most efficient method of connecting telephone calls is to route them directly, which only requires one trunk per call. This is particularly important when trunking resources become more valuable as the network approaches operational capacity. At this stage, more calls begin to overflow and connect via their multi-link paths, which prevents future calls from connecting on their direct paths. One solution to limit excessive use of multi-link paths is to use an efficient and simple control mechanism called trunk reservation.

2. TRUNK RESERVATION

In a trunk reservation system, a number of trunks in a trunk group are reserved for direct calls only. Direct calls are also allowed to connect on the non-reserved trunks but they can only use the reserved trunks when all the non-reserved trunks are occupied. Multi-link calls are only allowed to connect on the non-reserved trunks.

An important characteristic of trunk reservation is that the decision to accept an incoming call is only dependent on the available capacity of the trunk group at the realization of the call and not on the entire state of the network (Hunt and Laws, 1997). One example of alternate-routing systems that is dependent on the state of the network is the dynamic routing system. Dynamic routing systems incorporate a form of trunk reservation in their routing-decision processes by automatically regenerating new alternate paths for an origin-destination switch pair when its current multi-link paths become congested. The interested reader is referred to Gibbens and Kelly (1990), Mitra and Gibbens (1992), and Mitra et al. (1993).

Trunk reservation is an intuitively sound concept and its optimality is demonstrated through Markov decision theory analysis of a single trunk group (Kelly, 1990). A trunk group is offered two classes of traffic: direct and multi-link calls. The transitions of the Markov decision process are dependent on the arrival rates of the two classes of traffic. A reward of r^sub 1^ is realized when a direct call is connected on the trunk group and a reward of r^sub 2^ is obtained if a multi-link call is connected, with r^sub 1^ > r^sub 2^ > 0. The states are the number of trunks occupied in the trunk group and the action is to either connect or not connect an incoming call. Finally, the objective of the Markov decision process is to maximize the long-run average expected reward per unit time. The resulting optimal policy is to accept direct calls if the trunk group is not full and to accept multi-link calls only if the number of trunks available in the trunk group is above an optimal value (Lippman, 1975; Miller, 1969). This optimal policy is essentially a trunk reservation policy, where a number of trunks in a trunk group is reserved solely for direct calls.

Trunk reservation controls congestion by reducing the overall loss probabilities (overflow), hence limiting multi-link calls in the network. Furthermore, it provides stability in the network by reducing the knock-off effects of multi-link paths (Kelly, 1990). Gibbens and Kelly (1990) find that using a small non-zero value for the trunk reservation parameter (generally 1% to 5% of trunk group size) significantly improves the loss probability. Increasing the trunk reservation parameter any higher provides relatively little additional benefits to the system.