TRUNK RESERVATION ANALYSIS OF TELUS' EDMONTON TELECOMMUNICATION NETWORK

INFOR, Aug 2003 by Sim, Thaddeus

Previous studies of trunk reservation in circuit-switched, alternate routing networks have focused on the theoretical aspects of trunk reservation. We are unaware of any published results of the application of trunk reservation in actual networks. In addition, the choice of trunk reservation values in those studies was generated using a uniform rule. For example, Krupp (1982) set the number of reserved trunks in each trunk group to [the square root of]n/2, where n is the trunk group capacity, and Akinpelu (1984) reserved 5% of the trunks in a trunk group, with a minimum of one trunk, for direct calls. We believe these "one size fits all" approaches are not suitable for non-symmetric networks.

In this paper, we propose a procedure to find trunk group specific reservation parameters for TELUS' Edmonton network using fixed-point approximations of a birth-death process. The Edmonton network is a non-symmetric, fully-connected network. A fully-connected network is one where every switch is connected to all other switches in the network. Our modelling approach is described in section 3 including some discussion on data issues. We discuss our solution methodology in section 4 and present the results from our study of trunk reservation in the TELUS Edmonton network in section 5. Also in section 5, we compare the performance of the network with our non-uniform trunk reservation values against networks where the trunk reservation parameters are set uniformly. Concluding remarks follow in section 6.

3. MODELLING THE TRUNK RESERVATION PROBLEM

We begin by modelling each trunk group in the network using fixed-point approximations of a birth-death process. We then analyze the network "by means of fixed-point approximations, which are based on the assumption that each link acts independently; the traffic streams which are Poisson when offered to the network remain Poisson when offered to the links by virtue of this assumption" (Morrison, 1996). Recall that the purpose of trunk reservation is to limit the amount of multi-link calls or alternatively, to reduce the amount of calls overflowing from their direct paths. The objective, therefore, is to find the optimal set of trunk reservation values that minimizes total expected overflow. The fixed-point approximations allow us to calculate the total expected overflow level in the network for different trunk reservation values.

Figure 1 shows the state transition diagram of a birth-death process of a single trunk group. State i represents the state where i trunks are occupied. The trunk group contains c trunks with r trunks reserved for first-routed traffic, which are calls that connect on the first path of a route (usually the direct path). Non-first-routed traffic are calls that connect on paths with route indices of 2 or higher. The transition from one state to another is dependent on the current state and the subsequent action in the trunk group. Calls arrive into the trunk group following a Poisson process with rate [lambda]^sub 1^ [lambda]^sub 2^, where [lambda]^sub 1^ and [lambda]^sub 2^ are the arrival rates of first-routed and non-first-routed traffic respectively. The arrival rates [lambda]^sub 1^ and [lambda]^sub 2^ are trunk group specific. From the definition of trunk reservation, the rate at which the number of occupied trunks increases (birth rate) depends on the current state of the trunk group. If there are unreserved trunks available (states O to c - r - 1), a transition rate of [lambda]^sub 1^ [lambda]^sub 2^ is used. When only reserved trunks are available (states c - r to c - 1), the number of occupied trunks in the trunk group increases at rate [lambda]^sub 1^. When a call is completed or terminated in the trunk group, the number of occupied trunks decreases. A call terminates at a rate of [mu] (the service or death rate), which is also trunk group specific.