A demonstration of the use of a unified service model for urban infrastructure networks

Planning interventions on urban infrastructure networks requires the consideration of costs of interventions and interruptions to the service provided by the infrastructure. It also requires taking into consideration how these costs and interruptions change due to the proximity of close networks. For example, it is less expensive to replace a gas pipe if the road is open, and, if a pipe is being replaced, there is a probability that the adjacent water pipe will be hit, resulting in a loss of service. Determining the optimal intervention programme for a single network is challenging as one has to consider all the objects within the network. Determining the optimal intervention programmes for multiple networks is even more challenging, particularly because the number of possible intervention programmes explodes. In this paper, the application of a unified model of the service provided by urban infrastructure networks to be used in the search for optimal intervention programmes on multiple networks simultaneously is presented. By using a single equation for all networks, the model enables an increase in the speed of calculation compared to traditional models, as a single equation can be used. The reductions in accuracy from more traditional models are discussed. Notation A m service on network m A p pipe diameter B fric (t) friction power at time t B in (t) input power at time t B leak (t) leaking power at time t B loss (t) lost service power at time t B m general service power on network m B m service power on network m B m,in (t) service power input for network m B m,out (t) service power output for network m B out (t) service output power at time t B rd,opt traffic power in an optimal case B rd,out traffic power in actual case boxcar(x,a,b) boxcar function C LOS,el monetised level of electricity service C LOS,gs monetised level of gas service C LOS,rd monetised level of road service C LOS,sw monetised level of sewer service C LOS,wa monetised level of water service C m service pressure on network m c fix,el fixed cost of electricity production c fix,gs fixed cost of gas production c fix,sw fixed cost of sewer operation c fix,wa fixed cost of water production c loss,rd additional cost of impossible trips c poll,sw per-unit cost of sewer overflow c prod,el per-unit cost of electricity production c prod,gs per-unit cost of gas production c prod,wa per-unit cost of water production c sell,el per-unit revenue for electricity (as metered) c sell,gs per-unit revenue for gas (as metered) c sell,wa per-unit revenue for water (as metered) c travel,rd average travel time cost per hour D ! flow vector D hyd hydraulic diameter D m service flow on network m D n,m service flow through object o n,m D h service flow in/out of node h E m service unit on network m f 0,n,m conductivity function of object o n,m at time 0 f D Darcy friction factor f M Moody friction factor G LOS,m cost occurred by the loss in the level of service for network m G LOS,m,fix fixed cost of operating the network g prod,m cost per service power unit produced g rcv,m revenue per service power unit received H(x) Heaviside function M network characteristic matrix m index variable for the network m Î 1,…,M m ij (with i = j) sum of the conductance of all objects connected to node h i m ij (with i ≠ j) conductance between nodes h i and h j o n,m index variable for object n Î 1,…,N from network m P ! pressure vector T gs gas temperature T w index for the time phase with w Î 1,…,W t index for time 269 Cite this article Kielhauser C and Adey BT (2020) A demonstration of the use of a unified service model for urban infrastructure networks. Infrastructure Asset Management 7(4): 269-281,