During the past two decades, several methodologies are endorsed to assess the compatibility of roadways for bicycle use under homogeneous traffic conditions. However, these methodologies cannot be adopted under heterogeneous traffic where on-street bicyclists encounter a complex interaction with various types of vehicles and show divergent operational characteristics. Thus, the present study proposes an initial model suitable for urban road segments in mid-sized cities under such complex situations. For analysis purpose, various operational and physical factors along with user perception data sets (13,624 effective ratings in total) were collected from 74 road segments. Eight important road attributes affecting the bicycle service quality were identified using the most recent and most promising machine learning technique namely, random forest. The identified variables are namely, effective width of outside through lane, pavement condition index, traffic volume, traffic speed, roadside commercial activities, interruptions by unauthorized stoppages of intermittent public transits, vehicular ingress-egress to on-street parking area, and frequency of driveways carrying a high volume of traffic. Service prediction models were developed using ordered probit and ordered logit modeling structures which meet a confidence level of 95%. Prediction performances of developed models were assessed in terms of several statistical parameters and the ordered probit model outperformed the ordered logit model. Incorporating outputs of the probit model, a predictive equation is presented that can identify under what level a segment is offering services for bicycle use. The service levels offered by roadways were classified into six categories varying from 'excellent' to 'worst' (A-F).

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We consider product of expansive Markov maps on an interval with hole which is conjugate to a subshift of finite type. For certain class of maps, it is known that the escape rate into a given hole does not just depend on its size but also on its position in the state space. We illustrate this phenomenon for maps considered here. We compare the escape rate into a connected hole and a hole which is a union of holes with a certain property, but have same measure. This gives rise to some interesting combinatorial problems.

We consider a subshift of finite type on q symbols with a union of t cylinders based at words of identical length p as the hole. We explore the relationship between the escape rate into the hole and a rational function, $r(z)$ , of correlations between forbidden words in the subshift with the hole. In particular, we prove that there exists a constant $D(t,p)$ such that if $q>D(t,p)$ , then the escape rate is faster into the hole when the value of the corresponding rational function $r(z)$ evaluated at $D(t,p)$ is larger. Further, we consider holes which are unions of cylinders based at words of identical length, having zero cross-correlations, and prove that the escape rate is faster into the hole with larger Poincaré recurrence time. Our results are more general than the existing ones known for maps conjugate to a full shift with a single cylinder as the hole.