A performance measure analysis for traffic networks with random data and general monotone cost functions

This paper studies the dependence structure and bounds of several basic prototypical parallel queueing systems with correlated arrival processes to different queues. The marked feature of our systems is that each queue viewed alone is a standard single-server queuing system extensively studied in the literature, but those queues are statistically dependent due to correlated arrival streams. The major difficulty in analysing those systems is that the presence of correlation makes the explicit computation of a joint performance measure either intractable or computationally intensive. In addition, it is not well understood how and in what sense arrival correlation will improve or deteriorate a system performance measure. The objective of this paper is to provide a better understanding of the dependence structure of correlated queueing systems and to derive computable bounds for the statistics of a joint performance measure. In this paper, we obtain conditions on arrival processes under which a performance measure in two systems can be compared, in the sense of orthant and supermodular orders, among different queues and over different arrival times. Such strong comparison results enable us to study both spatial dependence (dependence among different queues) and temporal dependence (dependence over different time instances) for a joint performance measure. Further, we derive a variety of upper and lower bounds for the statistics of a stationary joint performance measure. Finally, we apply our results to synchronized queueing systems, using the ideas combined from the theory of orthant and supermodular dependence orders and majorization with respect to weighted trees (Xu and Li (2000)). Our results reveal how a performance measure can be affected, favourably or adversely, by different types of dependencies.

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Incentives and Innovation: A Multitasking Approach

American Economic Journal Microeconomics ◽

10.1257/mic.3.1.78 ◽

2011 ◽

Vol 3 (1) ◽

pp. 78-128 ◽

Cited By ~ 25

Author(s):

Thomas Hellmann ◽

Veikko Thiele

Keyword(s):

Intellectual Property ◽

Property Rights ◽

Intellectual Property Rights ◽

Performance Metrics ◽

Performance Measure ◽

Ex Post ◽

A Performance

This paper develops a multitask model where employees make choices between their assigned standard tasks, for which the firm has a performance measure and provides incentives, and privately observed innovation opportunities that fall outside of the performance metrics, and require ex post bargaining. If innovations are highly firm specific, firms provide lower-powered incentives for standard tasks to encourage more innovation, yet in equilibrium employees undertake too few innovations. The opposite occurs if innovations are less firm specific. We also investigate the effectiveness of several possibilities to encourage innovation, such as tolerance for failure, stock-based compensation, and the allocation of intellectual property rights. (JEL D21, J33, M12, O31, O34)

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