*John P. Lehoczky*

My main research interests involve the theory of stochastic processes, i.e. the evolution of random phenomena over time, and the use of stochastic processes to model real applications. I use stochastic process models to study a wide range of phenomena including the modelling and control of computer systems, communication networks and manufacturing facilities. My recent work is focused on developing methods that combine system scheduling with performance evaluation. For example, in a manufacturing system, the products will have deadlines for delivery or in a real-time computer or communication system certain tasks must be completed within stringent timing requirements, say in ATM networks or multimedia systems. My collaborations in these two problems involve faculty and graduate students in the CMU Department of Electrical and Computer Engineering, the College of Computer Science, and the Software Engineering Institute, who are building and testing systems which embody some of the theory I have developed.

A different research interest involves the application of stochastic modelling to problems in finance. My initial work was done jointly with Steven Shreve of the CMU mathematics department and Ioannis Karatzas of Columbia University. Together, we developed equilibrium-based models for stock and bond prices. More recently, I have been one of four organizers of the new CMU Masters Degree program in Computational Finance. Within this program I have been teaching and doing research on developing simulation methods for option pricing.

I am involved in a variety of other applications. For example, I collaborate on a large cardiovascular treatment study being conducted by the University of Pittsburgh Medical School. In one part of the study, subjects generate 24-hour ambulatory blood pressure and heart rate recordings. We are studying these complex data sets to better understand the role that biological rhythms, subject activities and treatments play in governing a subject's blood pressure. I also participate in the Industrial Statistics activities of the Department. I am particularly interested in the VLSI wafer fabrication project, because it allows me to combine my interests in stochastic models with statistical inference. Some recent representative publications in each of these areas are given below.

*Some Related Publications*

Kruk, L., Lehoczky, J., Ramanan, K., and Shreve, S. (2011) ``Heavy Traffic Analysis for EDF Queues with Reneging,'' *Annals of Applied Probability*, 21(2), 484-545.

Kruk, L., Lehoczky, J., Ramanan, K., and Shreve, S. (2009) ``Double Skorokhod map and reneging in real-time queues,'' Markov Processes and Related Topics: A Festscrhrift for Thomas G. Kurtz, Inst. Math. Statist., Lecture Notes -- Monograph Series,Vol.4, Ethier, S., Feng, J., and Stockbridge, R. (eds.), 169-193.<;>

Lakshmanan, K., Rajkumar, R., and Lehoczky, J.P. (2009) ``Partitioned fixed-priority preemptive scheduling for multi-core processors,'' 21st Euromicro Conference on Real-Time Systems (ECRTS), July.

Kruk, L., Lehoczky, J., Ramanan, K., and Shreve, S. (2007) ``An explicit
formula for doubly reflected processes on [0,a],'' *Annals of
Probability*, 35, 1740-1768.

Serban, M., Lehoczky, J., and
Brockwell, A., (2007) ``Modeling the dynamic dependence structure in
multivariate financial time series,'' *Journal of Time Series Analysis*,
28, 763-782.

Lehoczky, J., (1996) "Real-time queueing theory," to appear
*Proceedings of the 18th IEEE Transactions on Real-Time Systems*,
December.

Stronsnider, J., Lehoczky, J. and Sha, L., (1995) "The deferrable
server algorithm for enhanced aperiodic responsiveness in real-time environments,"
*IEEE Transactions on Computers*, **44**, No. 1, January, pp. 73-91.

Lehoczky, J., (1996) "Simulation methods for option pricing,"
to appear, *Proceedings, Bank of England Conference on Mathematical Finance*,
Springer-Verlag.

Rao, S., Lehoczky, J., Schervish, M. and Strojwas, A. (1995) "A Bayesian
approach to monitoring multi-stage manufacturing processes," *Computing
Science and Statistics*, **27**, pp. 34-44.