The efficient use of available resources is a key factor in achieving success on both personal and organizational levels. One of the crucial resources in knowledge economy is time. The ability to force others to adapt to our schedule even if it harms their efficiency can be seen as an outcome of social stratification. The principal objective of this paper is to use time allocation to model and study the global efficiency of social stratification, and to reveal whether hierarchy is an emergent property. A multi-agent model with an evolving social network is used to verify our hypotheses. The network's evolution is driven by the intensity of inter-agent communications, and the communications as such depend on the preferences and time resources of the communicating agents. The entire system is to be perceived as a metaphor of a social network of people regularly filling out agenda for their meetings for a period of time. The overall efficiency of the network of those scheduling agents is measured by the average utilization of the agent's preferences to speak on specific subjects. The simulation results shed light on the effects of different scheduling methods, resource availabilities, and network evolution mechanisms on communication system efficiency. The non-stratified systems show better long-term efficiency. Moreover, in the long term hierarchy disappears in overwhelming majority of cases. Some exceptions are observed for cases where privileges are granted on the basis of node degree weighted by relationship intensities but only in the short term.