On the minimal travel time needed to collect n items on a circle

Annals of Applied Probability

Volumn 14, Issue 2, 2004, Pages 881-902

  Litvak, Nelly ^a   Van Zwet, Willem R ^b  

^a UNIVERSITY OF TWENTE   (Netherlands)

^b LEIDEN UNIVERSITY   (Netherlands)

Author keywords

Asymptotics; Carousel systems; Exact distributions; Exponential functionals; Uniform spacings

Indexed keywords

EID: 26844558644     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/105051604000000152     Document Type: Article

References (18)

1. ALI, M. M. and OBAIDULLAH, M. (1982). Distribution of linear combination of exponential variates. Comm. Statist. Theory Methods 11 1453-1463.
2. ASKEY, R. (1980). Ramanujan's extensions of the gamma and beta functions. Amer. Math. Monthly 87 346-359.
3. BARTHOLDI, J. J. III and PLATZMAN, L. K. (1986). Retrieval strategies for a carousel conveyor. IIE Transactions 18 166-173.
4. BERTOIN, J. and YOR, M. (2001). On subordinators, self-similar Markov processes and some factorizations of the exponential variable. Electron. Comm. Probab. 6 95-106.
5. BERTOIN, J. and YOR, M. (2002a). On the entire moments of self-similar Markov processes and exponential functionals of Lévy processes. Ann. Fac. Sci. Toulouse Math. (6) 11 33-45.
6. BERTOIN, J. and YOR, M. (2002b). The entrance laws of self-similar Markov processes and exponential functionals of Lévy processes. Potential Anal. 17 389-400.
7. BERTOIN, J., BIANE, P. and YOR, M. (2002). Poissonian exponential functionals, q-series, q-integrals, and the moment problem for log-normal distributions. Technical Report PMA-705, Univ. Paris 6, Laboratoire de Probabilités.
8. CARMONA, P., PETIT, F. and YOR, M. (1997). On the distribution and asymptotic results for exponential functionals of Lévy processes. In Exponential Functionals and Principal Values Related to Brownian Motion (M. Yor, ed.) 73-130. Iberoamericana, Madrid.
9. DAVIS, R. A. and RESNICK, S. I. (1991). Extremes of moving averages of random variables with finite endpoint. Ann. Probab. 19 312-328.
10. DUMAS, V., GUILLEMIN, F. and ROBERT, PH. (2002). A Markovian analysis of additive-increase multiplicative-decrease algorithms. Adv. in Appl. Probab. 34 85-111.
11. FELLER, W. (1970). An Introduction to Probability Theory and Its Applications II. Wiley, London.
12. GASPER, G. and RAHMAN, M. (1990). Basic Hypergeometric Series. Cambridge Univ. Press.
13. GUILLEMIN, F., ROBERT, PH. and ZWART, B. (2002). AIMD algorithms and exponential functionals. Technical Report 4447, INRIA.
14. LITVAK, N. and ADAN, I. (2001). The travel time in carousel systems under the nearest item heuristic. J. Appl. Probab. 38 45-54.
15. LITVAK, N. and ADAN, I. (2002). On a class of order pick strategies in paternosters. Oper. Res. Lett. 30 377-386.
16. LITVAK, N. (2001). Some peculiarities of exponential random variables. J. Appl. Probab. 38 787-792.
17. PYKE, R. (1965). Spacings. J. R. Stat. Soc. Ser. B Stat. Methodol. 27 395-449.
18. YOR, M. (2001). Exponential Functionals of Brownian Motion and Related Processes. Springer, Berlin.