Recursive Utility for Stochastic Trees

Abstract

This work is important for several reasons. It is the first contribution to the literature on preference over risky time streams in which the utility structure is linked to specific and frequently used stochastic models (stochastic trees), and in which the utility structure is specifically designed to permit tractable methods of expected utility calculation (dynamic programming recursion). The stochastic tree structure with utility recursion is important because it extends the convenient graphical features of decision trees to the modeling of risky time streams. Such features include ease and clarity in model formulation and presentation, as well as a visual structure which suggests a computational method of solution (rollback). In the near term, this provides graphically intuitive model construction and evaluation capabilities for users who may be less familiar with stochastic modeling and algorithms, especially including users those in the medical community, for whom this tool was developed. The results of the paper characterize all possible recursive utility functions over stochastic trees, providing in the long term a basis for devising useful utility structures beyond what are discussed in the paper.

Intersystem Soft Handover for Converged DVB-H and UMTS Networks

“…Using (24) and (25), the expected total QAST and the expected total COST for UMTS and DVB-H can be calculated. Therefore, the tradeoff between the QAST and the COST can be obtained.…”

“…Practical parameter values can be used in the model after real field tests in the network planning and optimization stage. From (24) and (25), the expected total COST and the expected total QAST for UMTS and DVB-H in the case of one user can be calculated along the two separate trunks of the stochastic tree as follows: For N users of the same service, suppose that N 1 users are using UMTS, and N 2 users are using DVB-H. The total COST and QAST for the converged network are C total = 5.4N 1 + 3.6 and Q total = 3.6N 1 + 3.3N 2 = 0.3N 1 + 3.3N , respectively.…”

“…In this paper, for the first time, stochastic trees are being used in the communications field to make handover decisions to predict the converged network operation cost and the network QoS that can be expected, given an initial network state and an established handover plan. An advantage of the stochastic tree model is that it allows the recursive computation of the mean quality-adjusted duration, which is the mean duration with quality weights, by "rolling back" the stochastic tree much as one would roll back a decision tree [25]. Before applying the stochastic tree model to our intersystem handover process, the Markovian rollback formula will be developed for this case.…”

“…Before applying the stochastic tree model to our intersystem handover process, the Markovian rollback formula will be developed for this case. Detailed information about the use of the Markovian rollback formula in a medical decision process is provided in [25]. The development of the Markovian rollback formula for the converged network is shown below.…”

“…For a Markov process, λ and r(x) can always be assumed as exponential distributions [25]. Then, the QAST after considering risk factor r(x) in state x per time unit is given by…”