Publications of Charles Knessl

Fannu Hu and Charles Knessl.  Asymptotics of American floating lookback put option pricing.  2016.
Charles Knessl.  An Erlang loss model with priorities: diffusion approximation, integral representations and asymptotic expansions.  2016.
Qiang Zhen, Johan S.H. van Leeuwaarden and Charles Knessl.  On the sojourn time distribution in a finite population Markovian processor sharing queue.  to appear in IMA Journal of Applied Mathematics.  2016.
Eunju Sohn and Charles Knessl.  On a storage allocation model with finite capacity.  to appear in European Journal of Applied Mathematics.  2016.
Eunju Sohn and Charles Knessl.  Asymptotic analysis of a storage allocation model with finite capacity: joint distribution.  Adv. Oper. Res., Art. ID 1925827(2016):56, 2016.
Eunju Sohn and Charles Knessl.  A diffusion limit for a finite capacity storage allocation model.  to appear in Applied Math Research Express (AMRX).  2016.
Eunju Sohn and Charles Knessl.  Asymptotic analysis of a storage allocation model with finite capacity: marginal and conditional distributions.  2016.
Qiang Zhen and Charles Knessl.  Some asymptotic results for the transient distribution of the Halfin-Whitt diffusion process.  European Journal of Applied Mathematics, 26(3):245--295, 2015.
Johan S. H. van Leeuwaarden and Charles Knessl.  Transient analysis of the Erlang A model.  Mathematical Methods of Operations Research, 82(2):143--173, 2015. . 
Charles Knessl and Haishen Yao.  A note on the transition from diffusion with the flow to diffusion against the flow, for first passage times in singularly perturbed drift-diffusion models.  Asymptotic Analysis, 91:205--231, 2015.
Charles Knessl and Haishen Yao.  On the nonsymmetric longer queue model II: marginal and conditional probabilities.  Applied Mathematics Research Express, 2015(1):1--47, 2015.
F. Guillemin, C. Knessl and J. S. H. van Leeuwaarden.  First response to letter of G. Fayolle and R. Iasnogorodski [\refcno 3152167].  Queueing Syst., 76(1):109--110, 2014. MR3152168
Brian Fralix, Charles Knessl and Johan S. H. van Leeuwaarden.  First passage times to congested states of many-server systems in the Halfin-Whitt regime.  Stoch. Models, 30(2):162--186, 2014. MR3202118
Philippe Jacquet, Charles Knessl and Wojciech Szpankowski.  A note on a problem posed by D. E. Knuth on a satisfiability recurrence.  Combin. Probab. Comput., 23(5):829--841, 2014. MR3249226
Fabrice Guillemin, Charles Knessl and Johan S. H. van Leeuwaarden.  Erratum to: Wireless three-hop networks with stealing II: exact solutions through boundary value problems [mr3054657].  Queueing Syst., 78(2):189--195, 2014. MR3256837
Charles Knessl.  Introduction to Queueing Systems with Telecommunications Applications, by Laslo Lakatos, Laszlo Szeidl, and Miklos Telek.  SIAM Review, 56(1):203--207, 2014. book review . 
Abram Magner, Charles Knessl and Wojciech Szpankowski.  Expected external profile of PATRICIA tries.  In Analco14—meeting on analytic algorithmics and combinatorics, pages 16--24.  SIAM, 2014.
Qiang Zhen and Charles Knessl.  An explicit solution to the chessboard pebbling problem.  J. Difference Equ. Appl., 19(2):201--208, 2013. MR3021782
Xiaoqian Tan, Charles Knessl and Yongzhi Yang.  On finite capacity queues with time dependent arrival rates.  Stochastic Process. Appl., 123(6):2175--2227, 2013. MR3038502
Fabrice Guillemin, Charles Knessl and Johan S. H. van Leeuwaarden.  Wireless three-hop networks with stealing II: exact solutions through boundary value problems.  Queueing Syst., 74(2-3):235--272, 2013. MR3054657
Charles Knessl and Haishen Yao.  On the nonsymmetric longer queue model: joint distribution, asymptotic properties, and heavy traffic limits.  Adv. Oper. Res., Art. ID 680539, 21, 2013. MR3055983
Qiang Zhen and Charles Knessl.  On spectral properties of finite population processor shared queues.  Math. Methods Oper. Res., 77(2):147--176, 2013. MR3070024
Qiang Zhen and Charles Knessl.  Asymptotic analysis of spectral properties of finite capacity processor shared queues.  Stud. Appl. Math., 131(2):179--210, 2013. MR3084693
Charles Knessl and John A. Morrison.  Asymptotic analysis of two coupled queues with vastly different arrival rates and finite customer capacities.  Stud. Appl. Math., 128(2):107--143, 2012. MR2896784
Charles Knessl and John A. Morrison.  Asymptotic analysis of two coupled large capacity queues with vastly different arrival rates.  Appl. Math. Res. Express. AMRX, 1:47--75, 2012. MR2900146
Sean Lynch and Charles Knessl.  Singular perturbation analysis of drift-diffusion past a circle: shadow region.  IMA J. Appl. Math., 77(2):252--278, 2012. MR2901191
Eunju Sohn and Charles Knessl.  Some exact and asymptotic solutions to single server models of dynamic storage.  Stoch. Models, 28(2):248--280, 2012. MR2926587
Charles Knessl.  \it {C}onstructive computation in stochastic models with applications [book review of mr2604162].  SIAM Rev., 54(1):193--196, 2012. MR2932299
Philippe Jacquet, Charles Knessl and Wojciech Szpankowski.  Counting Markov types, balanced matrices, and Eulerian graphs.  IEEE Trans. Inform. Theory, 58(7):4261--4272, 2012. MR2943088
Yongwook Choi, Charles Knessl and Wojciech Szpankowski.  A new binomial recurrence arising in a graphical compression algorithm.  In 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12), pages 1--12.  Assoc. Discrete Math. Theor. Comput. Sci., Nancy, 2012. MR2957316
Diego Dominici and Charles Knessl.  Asymptotic analysis of a family of polynomials associated with the inverse error function.  Rocky Mountain J. Math., 42(3):847--872, 2012. MR2966475
Yongwook Choi, Charles Knessl and Wojciech Szpankowski.  On a recurrence arising in graph compression.  Electron. J. Combin., 19(3):Paper 15, 22, 2012. MR2967220
Haishen Yao and Charles Knessl.  On the finite capacity shortest queue problem.  Progress in Applied Mathematics, 2(1):1-34, 2012.
Johan van Leeuwaarden and Charles Knessl.  Spectral gap in the Erlang A model in the Halfin-Whitt regime.  Stochastic Systems, 2:149--207, 2012. (electronic; DOI: 10.1214/10-SSY012). 
Charles Knessl and Mark W. Coffey.  An effective asymptotic formula for the Stieltjes constants.  Math. Comp., 80(273):379--386, 2011. MR2728984
Eunju Sohn and Charles Knessl.  Storage allocation under processor sharing II: further asymptotic results.  European J. Appl. Math., 22(1):45--82, 2011. MR2771025
Miao Xu and Charles Knessl.  On a free boundary problem for an American put option under the CEV process.  Appl. Math. Lett., 24(7):1191--1198, 2011. MR2784181
Charles Knessl and John A. Morrison.  Two coupled queues with vastly different arrival rates: critical loading case.  Adv. Oper. Res., Art. ID 216790, 26, 2011. MR2794085
Johan S. H. van Leeuwaarden and Charles Knessl.  Transient behavior of the Halfin-Whitt diffusion.  Stochastic Process. Appl., 121(7):1524--1545, 2011. MR2802464
Charles Knessl and Mark W. Coffey.  An asymptotic form for the Stieltjes constants $\gamma_{k}(a)$ and for a sum $S_{\gamma}(n)$ appearing under the Li criterion.  Math. Comp., 80(276):2197--2217, 2011. MR2813355
Fabrice Guillemin, Charles Knessl and Johan S. H. van Leeuwaarden.  Wireless multihop networks with stealing: large buffer asymptotics via the ray method.  SIAM J. Appl. Math., 71(4):1220--1240, 2011. MR2823500
Zhilong Zhang and Charles Knessl.  Enumeration of general t-ary trees and universal types.  Progress in Applied Mathematics, 1:1-70, 2011.
Eunju Sohn and Charles Knessl.  On some simple single server models of dynamic storage.  In QTNA '11: Proceedings of the 6th International Conference on Queueing Theory and Network Applications , pages 161--168.  ACM, 2011.
Qiang Zhen and Charles Knessl.  Asymptotic expansions for the sojourn time distribution in the $M/G/1$-PS queue.  Math. Methods Oper. Res., 71(2):201--244, 2010. MR2606922
Eunju Sohn and Charles Knessl.  Storage allocation under processor sharing I: exact solutions and asymptotics.  Queueing Syst., 65(1):1--18, 2010. MR2610611
S. Lynch and C. Knessl.  Drift-diffusion past an ellipse: singular perturbation analysis of the illuminated region.  Stud. Appl. Math., 125(2):113--151, 2010. MR2676128
Philippe Jacquet, Charles Knessl and Wojciech Szpankowski.  Counting Markov types.  In 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), pages 387--400.  Assoc. Discrete Math. Theor. Comput. Sci., Nancy, 2010. MR2732021
Qiang Zhen, Johan S. H. van Leeuwaarden and Charles Knessl.  On a processor sharing queue that models balking.  Math. Methods Oper. Res., 72(3):453--476, 2010. MR2739053
Fannu Hu and Charles Knessl.  Asymptotics of barrier option pricing under the CEV process.  Appl. Math. Finance, 17(3):261--300, 2010. MR2786962
Fabrice Guillemin, Charles Knessl and Johan van Leeuwaarden.  Wireless multi-hop networks with stealing: Large buffer asymptotics.  In Teletraffic Congress (ITC), 22nd international, pages 1-8.  2010.
Charles Knessl and John A. Morrison.  A two-dimensional diffusion approximation for a loss model with trunk reservation.  SIAM J. Appl. Math., 69(5):1457--1476, 2009. MR2487068
Sean Lynch and Charles Knessl.  Drift-diffusion past a circle: shadow region asymptotics.  SIAM J. Appl. Math., 69(6):1559--1579, 2009. MR2487161
John A. Morrison and Charles Knessl.  Asymptotic analysis of a loss model with trunk reservation. II. Trunks reserved for slow traffic.  Stud. Appl. Math., 122(2):153--193, 2009. MR2492864
Qiang Zhen and Charles Knessl.  On sojourn times in the finite capacity $M/M/1$ queue with processor sharing.  Oper. Res. Lett., 37(6):447--450, 2009. MR2552723
Charles Knessl and Wojciech Szpankowski.  On the average profile of symmetric digital search trees.  Online J. Anal. Comb., 4:Art. 6, 14, 2009. MR2575176
Qiang Zhen and Charles Knessl.  On sojourn times in the $M/M/1$-PS model, conditioned on the number of other users.  Appl. Math. Res. Express. AMRX, 2:142--167, 2009. MR2607404
John A. Morrison and Charles Knessl.  Asymptotic analysis of a loss model with trunk reservation. I. Trunks reserved for fast traffic.  J. Appl. Math. Stoch. Anal., Art. ID 415692, 34, 2008. MR2377796
Charles Knessl.  On the number of reachable configurations for the chessboard pebbling problem.  Math. Comput. Modelling, 47(1-2):127--139, 2008. MR2382405
Haishen Yao and Charles Knessl.  On the shortest queue version of the Erlang loss model.  Stud. Appl. Math., 120(2):129--212, 2008. MR2387337
Haishen Yao and Charles Knessl.  Some first passage time problems for the shortest queue model.  Queueing Syst., 58(2):105--119, 2008. MR2390270
Eunju Sohn and Charles Knessl.  A simple direct solution to a storage allocation model.  Appl. Math. Lett., 21(2):172--175, 2008. MR2426974
Eunju Sohn and Charles Knessl.  The distribution of wasted spaces in the $M/M/\infty$ queue with ranked servers.  Adv. in Appl. Probab., 40(3):835--855, 2008. MR2454035
Charles Knessl and Diego Ernesto Dominici.  Asymptotic analysis of a fluid model modulated by an $M/M/1$ queue.  Adv. in Appl. Probab., 40(3):856--881, 2008. MR2454036
Charles Knessl and Wojciech Szpankowski.  On some non-linear recurrences that arise in computer science.  In Frontiers of applied and computational mathematics, pages 172--181.  World Sci. Publ., Hackensack, NJ, 2008. MR2503686
Fannu Hu and Charles Knessl.  Asymptotics of American barrier option pricing.  Can. Appl. Math. Q., 16(4):379--399, 2008. MR2656214
Qiang Zhen and Charles Knessl.  Asymptotic expansions for the conditional sojourn time distribution in the $M/M/1$-PS queue.  Queueing Syst., 57(4):157--168, 2007. MR2369215
Charles Knessl and Yongzhi Yang.  On the Erlang loss model with time dependent input.  Queueing Syst., 52(1):49--104, 2006. MR2201625
Haishen Yao and Charles Knessl.  On the infinite server shortest queue problem: non-symmetric case.  Queueing Syst., 52(2):157--177, 2006. MR2219952
Charles Knessl and Wojciech Szpankowski.  On the joint path length distribution in random binary trees.  Stud. Appl. Math., 117(2):109--147, 2006. MR2241984
Diego Dominici and Charles Knessl.  Ray solution of a singularly perturbed elliptic PDE with applications to communications networks.  SIAM J. Appl. Math., 66(6):1871--1894 (electronic), 2006. MR2262956
Charles Knessl and Wojciech Szpankowski.  Binary trees, left and right paths, WKB expansions, and Painlevé transcendents.  In Proceedings of the Eighth Workshop on Algorithm Engineering and Experiments and the Third Workshop on Analytic Algorithmics and Combinatorics, pages 198--204.  SIAM, Philadelphia, PA, 2006. MR2498159
Diego Dominici and Charles Knessl.  Geometrical optics approach to Markov-modulated fluid models.  Stud. Appl. Math., 114(1):45--93, 2005. MR2117327
Haishen Yao and Charles Knessl.  On the infinite server shortest queue problem: symmetric case.  Stoch. Models, 21(1):101--132, 2005. MR2124361
Charles Knessl and John A. Morrison.  Blocking probabilities for an underloaded or overloaded link with trunk reservation.  SIAM J. Appl. Math., 66(1):82--97 (electronic), 2005. MR2179743
Charles Knessl and Wojciech Szpankowski.  Enumeration of binary trees and universal types.  Discrete Math. Theor. Comput. Sci., 7(1):313--400 (electronic), 2005. MR2192041
Charles Knessl.  Elements of Queueing Theory: Palm Martingale and Stochastic Recurrences (Second edition), by Francois Bacelli and Pierre Bremaud.  SIAM Review, 47:836--837, 2005. book review. 
Charles Knessl and Wojciech Szpankowski.  Enumeration of binary trees, Lempel-Ziv '78 parsing, and universal types.  In Proc. of the second workshop on analytic algorithmics and combinatorics (Analco 05), pages 222--229.  SIAM, 2005.
D. Dominici and C. Knessl.  A small elliptic perturbation of a backward-forward parabolic problem with applications to stochastic models.  Appl. Math. Lett., 17(5):535--542, 2004. MR2057346
Diego Dominici and Charles Knessl.  Asymptotic analysis by the saddle point method of the Anick-Mitra-Sondhi model.  J. Appl. Math. Stoch. Anal., 1:19--71, 2004. MR2068379
Charles Knessl.  Some asymptotic results for the $M/M/\infty$ queue with ranked servers.  Queueing Syst., 47(3):201--250, 2004. MR2078410
Charles Knessl and Wojciech Szpankowski.  On the number of full levels in tries.  Random Structures Algorithms, 25(3):247--276, 2004. MR2086160
Charles Knessl and John A. Morrison.  Heavy traffic analysis of two coupled processors.  Queueing Syst., 43(3):173--220, 2003. MR1968783
Charles Knessl.  Geometrical optics and models of computer memory fragmentation.  Stud. Appl. Math., 111(2):185--238, 2003. MR1990238
Charles Knessl.  Numerical studies of the asymptotic height distribution in binary search trees.  Discrete Math. Theor. Comput. Sci., 6(1):91--99 (electronic), 2003. MR2001156
Charles Knessl and Yongzhi Peter Yang.  An exact solution for an $M(t)/M(t)/1$ queue with time-dependent arrivals and service.  Queueing Syst., 40(3):233--245, 2002. MR1897711
Charles Knessl and Wojciech Szpankowski.  Limit laws for the height in PATRICIA tries.  J. Algorithms, 44(1):63--97, 2002. MR1932678
Charles Knessl and Wojciech Szpankowski.  The height of a binary search tree: the limiting distribution perspective.  Theoret. Comput. Sci., 289(1):649--703, 2002. MR1932916
Charles Knessl.  Asymptotic analysis of the American call option with dividends.  European J. Appl. Math., 13(6):587--616, 2002. MR1949725
Charles Knessl, Doo Il Choi and Charles Tier.  A dynamic priority queue model for simultaneous service of two traffic types.  SIAM J. Appl. Math., 63(2):398--422 (electronic), 2002. MR1951945
Charles Knessl.  Fundamentals of Queueing Networks: Performance, Asymptotics and Optimization, by Hong Chen and David D. Yao.  SIAM Review, 44:496--500, 2002. book review. 
C. Knessl.  Geometrical optics and chessboard pebbling.  Appl. Math. Lett., 14(3):365--373, 2001. MR1820626
Charles Knessl and Charles Tier.  A simple fluid model for servicing priority traffic.  IEEE Trans. Automat. Control, 46(6):909--914, 2001. MR1836487
Charles Knessl.  A note on a moving boundary problem arising in the American put option.  Stud. Appl. Math., 107(2):157--183, 2001. MR1842603
Charles Knessl.  On two-dimensional convection-diffusion past a circle.  SIAM J. Appl. Math., 62(1):310--335 (electronic), 2001. MR1857547
Charles Knessl and Yongzhi Yang.  Analysis of a Brownian particle moving in a time-dependent drift field.  Asymptot. Anal., 27(3-4):281--319, 2001. MR1858919
Charles Knessl and Yongzhi Peter Yang.  Asymptotic expansions for the congestion period for the $M/M/\infty$ queue.  Queueing Syst., 39(2-3):213--256, 2001. MR1870866
Charles Knessl.  Asymptotic and numerical studies of the leader election algorithm.  European J. Appl. Math., 12(6):645--664, 2001. MR1877345
Charles Knessl.  Elementary Lectures in Statistical Mechanics, by George D. J. Phillies.  SIAM Review, 43(2):390--391, 2001. book review. 
Charles Knessl and Joseph B. Keller.  Probability of Brownian motion hitting an obstacle.  SIAM J. Appl. Math., 60(2):729--745 (electronic), 2000. MR1740265
Charles Knessl and Joseph B. Keller.  Ray solution of a backward-forward parabolic problem for data-handling systems.  European J. Appl. Math., 11(1):1--12, 2000. MR1750386
Charles Knessl and Wojciech Szpankowski.  Height in a digital search tree and the longest phrase of the Lempel-Ziv scheme.  In Proceedings of the Eleventh Annual ACM-SIAM Symposium on Discrete Algorithms (San Francisco, CA, 2000), pages 187--196.  ACM, New York, 2000. MR1754856
Charles Knessl.  Exact and asymptotic solutions to a PDE that arises in time-dependent queues.  Adv. in Appl. Probab., 32(1):256--283, 2000. MR1765160
Charles Knessl.  Asymptotic expansions for a stochastic model of queue storage.  Ann. Appl. Probab., 10(2):592--615, 2000. MR1768221
Charles Knessl and Wojciech Szpankowski.  Asymptotic behavior of the height in a digital search tree and the longest phrase of the Lempel-Ziv scheme.  SIAM J. Comput., 30(3):923--964 (electronic), 2000. MR1778293
Charles Knessl and Wojciech Szpankowski.  A note on the asymptotic behavior of the heights in $b$-tries for $b$ large.  Electron. J. Combin., 7:Research Paper 39, 16 pp. (electronic), 2000. MR1779936
Charles Knessl.  Asymptotic analysis of a backward-forward parabolic problem for data-handling systems.  SIAM J. Appl. Math., 61(3):914--933 (electronic), 2000. MR1788024
Charles Knessl.  Geometric optics approach to first-passage distributions: caustic boundaries and exponentially small eigenvalues.  Stud. Appl. Math., 105(4):301--332, 2000. MR1793344
C. Knessl and W. Szpankowski.  Heights in generalized tries and PATRICIA tries.  In Latin' 2000 (Punta del este, uruguay), Lecture Notes in Computer Science, No. 1776, pages 298--307.  2000.
Charles Knessl and Charles Tier.  A ray approximation to a PDE that arises in the study of tandem queues.  Stud. Appl. Math., 102(1):87--120, 1999. MR1666680
Charles Knessl and Charles Tier.  A diffusion model for two tandem queues with general renewal input.  Comm. Statist. Stochastic Models, 15(2):299--343, 1999. MR1683607
Charles Knessl and Wojciech Szpankowski.  Quicksort algorithm again revisited.  Discrete Math. Theor. Comput. Sci., 3(2):43--63 (electronic), 1999. MR1685649
Doo Il Choi, Charles Knessl and Charles Tier.  A queueing system with queue length dependent service times, with applications to cell discarding in ATM networks.  J. Appl. Math. Stochastic Anal., 12(1):35--62, 1999. MR1690182
Charles Knessl and Wojciech Szpankowski.  Quicksort algorithm again revisited.  Discrete Math. Theor. Comput. Sci., 3(2):43--64 (electronic), 1999. MR1695194
Charles Knessl and Charles Tier.  Two tandem queues with general renewal input. I. Diffusion approximation and integral representations.  SIAM J. Appl. Math., 59(6):1917--1959 (electronic), 1999. MR1709792
Charles Knessl and Charles Tier.  Two tandem queues with general renewal input. II. Asymptotic expansions for the diffusion model.  SIAM J. Appl. Math., 59(6):1960--1997 (electronic), 1999. MR1709793
Charles Knessl.  A new heavy traffic limit for the asymmetric shortest queue problem.  European J. Appl. Math., 10(5):497--509, 1999. MR1727843
Charles Knessl.  A diffusion model for two parallel queues with processor sharing: transient behavior and asymptotics.  J. Appl. Math. Stochastic Anal., 12(4):311--338, 1999. MR1736072
C. Knessl.  Integral representations and asymptotic expansions for Shannon and Renyi entropies.  Appl. Math. Lett., 11(2):69--74, 1998. MR1609684
Charles Knessl and Charles Tier.  Heavy traffic analysis of a Markov-modulated queue with finite capacity and general service times.  SIAM J. Appl. Math., 58(1):257--323 (electronic), 1998. MR1610068
Daljit S. Ahluwalia, Joseph B. Keller and Charles Knessl.  Advection-diffusion around a curved obstacle.  J. Math. Phys., 39(7):3694--3710, 1998. MR1630573
Charles Knessl.  An explicit solution to a tandem queueing model.  Queueing Systems Theory Appl., 30(3-4):261--272, 1998. MR1672131
C. Knessl.  A note on the asymptotic behavior of the depth of tries.  Algorithmica, 22(4):547--560, 1998. MR1701628
Charles Knessl and Wojciech Szpankowski.  Quicksort again revisited.  In Randomization and approximation techniques in computer science (Barcelona, 1998), pages 346--356.  Springer, Berlin, 1998. MR1729181
Charles Knessl and Charles Tier.  Asymptotic approximations and bottleneck analysis in product form queueing networks with large populations.  Performance Evaluation, 33:219--248, 1998.
Charles Knessl and Joseph B. Keller.  Advection diffusion past a strip. I. Normal incidence.  J. Math. Phys., 38(1):267--282, 1997. MR1424654
Charles Knessl and Joseph B. Keller.  Advection-diffusion past a strip. II. Oblique incidence.  J. Math. Phys., 38(2):902--925, 1997. MR1434217
Xiaoqian Tan and Charles Knessl.  Integral representations and asymptotics for infinite- and finite-capacity queues described by the unfinished work. I.  SIAM J. Appl. Math., 57(3):791--823, 1997. MR1450849
Xiaoqian Tan and Charles Knessl.  Integral representations and asymptotics for infinite- and finite-capacity queues described by the unfinished work. II.  SIAM J. Appl. Math., 57(3):824--870, 1997. MR1450850
Yongzhi Yang and Charles Knessl.  Asymptotic analysis of the $M/G/1$ queue with a time-dependent arrival rate.  Queueing Systems Theory Appl., 26(1-2):23--68, 1997. MR1480866
Charles Knessl and Charles Tier.  Mean time for the development of large workloads and large queue lengths in the $GI/G/1$ queue.  J. Appl. Math. Stochastic Anal., 9(2):107--142, 1996. MR1392371
Charles Knessl and Craig Steven Peters.  Exact and asymptotic solutions for the time-dependent problem of collective ruin. II.  SIAM J. Appl. Math., 56(5):1471--1521, 1996. MR1409129
Charles Knessl and Charles Tier.  Asymptotic properties of first passage times for two tandem queues: time to empty the system.  Comm. Statist. Stochastic Models, 12(4):633--672, 1996. MR1410850
Xiaoming Tan and Charles Knessl.  A fork-join queueing model: diffusion approximation, integral representations and asymptotics.  Queueing Systems Theory Appl., 22(3-4):287--322, 1996. MR1414666
Yongzhi Yang and Charles Knessl.  Heavy traffic asymptotics of the queue length in the $GI/M/1-K$ queue.  European J. Appl. Math., 7(5):519--543, 1996. MR1419647
Charles Knessl and Charles Tier.  Asymptotic properties of first passage times for tandem Jackson networks. I. Buildup of large queue lengths.  Comm. Statist. Stochastic Models, 11(1):133--162, 1995. MR1316772
Charles Knessl and Joseph B. Keller.  Rossby waves.  Stud. Appl. Math., 94(4):359--376, 1995. MR1330881
Charles Knessl and Joseph B. Keller.  Stability of linear shear flows in shallow water.  J. Fluid Mech., 303:203--214, 1995. MR1363794
Charles Knessl and Charles Tier.  Applications of singular perturbation methods in queueing.  In Advances in queueing, pages 311--336.  CRC, Boca Raton, FL, 1995. MR1395164
Charles Knessl.  Asymptotic behavior of high-order differences of the plane partition function.  Discrete Math., 126(1-3):179--193, 1994. MR1264486
Charles Knessl.  On the distribution of the maximum number of broken machines for the repairman problem.  SIAM J. Appl. Math., 54(2):508--547, 1994. MR1265240
Charles Knessl and Charles Tier.  A processor-shared queue that models switching times: heavy usage asymptotics.  SIAM J. Appl. Math., 54(3):854--875, 1994. MR1274231
Charles Knessl, Charles Tier, B. J. Matkowsky and Z. Schuss.  A state-dependent $GI/G/1$ queue.  European J. Appl. Math., 5(2):217--241, 1994. MR1285040
Yongzhi Yang and Charles Knessl.  The unconditional sojourn time distribution in the queue $GI/M/1$-$K$ with processor sharing service.  Stud. Appl. Math., 93(1):29--91, 1994. MR1291361
Charles Knessl and Craig Steven Peters.  Exact and asymptotic solutions for the time-dependent problem of collective ruin. I.  SIAM J. Appl. Math., 54(6):1745--1767, 1994. MR1301280
Xiaoming Tan and Charles Knessl.  Heavy traffic asymptotics for a gated, infinite-server queue with uniform service times.  SIAM J. Appl. Math., 54(6):1768--1779, 1994. MR1301281
Shisheng Xie and Charles Knessl.  On the transient behavior of the $M/M/1$ and $M/M/1/K$ queues.  Stud. Appl. Math., 88(3):191--240, 1993. MR1204871
Xiaoming Tan and Charles Knessl.  A finite capacity PS queue which models switching times.  SIAM J. Appl. Math., 53(2):491--554, 1993. MR1212762
Shisheng Xie and Charles Knessl.  On the transient behavior of the Erlang loss model: heavy usage asymptotics.  SIAM J. Appl. Math., 53(2):555--599, 1993. MR1212763
Yongzhi Yang and Charles Knessl.  Conditional sojourn time moments in the finite capacity $GI/M/1$ queue with processor-sharing service.  SIAM J. Appl. Math., 53(4):1132--1193, 1993. MR1232171
Xiaoming Tan, Yongzhi Yang and Charles Knessl.  The conditional sojourn time distribution in the $GI/M/1$ processor-sharing queue in heavy traffic.  Queueing Systems Theory Appl., 14(1-2):99--109, 1993. MR1238664
Joseph B. Keller and Charles Knessl.  Asymptotic evaluation of oscillatory sums.  European J. Appl. Math., 4(4):361--379, 1993. MR1251820
Xiaoming Tan and Charles Knessl.  Sojourn time distribution in some processor-shared queues.  European J. Appl. Math., 4(4):437--448, 1993. MR1251824
Charles Knessl.  On the sojourn time distribution in a finite capacity processor shared queue.  J. Assoc. Comput. Mach., 40(5):1238--1301, 1993. MR1368965
Charles Knessl.  Asymptotic approximations for the $GI/M/1$ queue with processor-sharing service.  Comm. Statist. Stochastic Models, 8(1):1--34, 1992. MR1159408
Charles Knessl and Charles Tier.  Asymptotic expansions for large closed queueing networks with multiple job classes.  IEEE Trans. Comput., 41(4):480--488, 1992. MR1163033
Charles Knessl and Charles Tier.  A processor-shared queue that models switching times: normal usage.  SIAM J. Appl. Math., 52(3):883--899, 1992. MR1163812
Charles Knessl and Joseph B. Keller.  Stability of rotating shear flows in shallow water.  J. Fluid Mech., 244:605--614, 1992. MR1192258
Charles Knessl and Joseph B. Keller.  Stirling number asymptotics from recursion equations using the ray method.  Stud. Appl. Math., 84(1):43--56, 1991. MR1082532
Charles Knessl.  On the diffusion approximation to a fork and join queueing model.  SIAM J. Appl. Math., 51(1):160--171, 1991. MR1089136
Charles Knessl and J. A. Morrison.  Heavy-traffic analysis of a data-handling system with many sources.  SIAM J. Appl. Math., 51(1):187--213, 1991. MR1089138
Charles Knessl and Joseph B. Keller.  Asymptotic properties of eigenvalues of integral equations.  SIAM J. Appl. Math., 51(1):214--232, 1991. MR1089139
Charles Knessl.  On the transient behavior of the repairman problem.  Adv. in Appl. Probab., 23(2):327--354, 1991. MR1104084
Charles Knessl.  The WKB approximation to the $G/M/m$ queue.  SIAM J. Appl. Math., 51(4):1119--1133, 1991. MR1117434
C. Knessl and J. A. Morrison.  Heavy-traffic analysis of the sojourn time in a three node Jackson network with overtaking.  Queueing Systems Theory Appl., 8(2):165--182, 1991. MR1118367
Charles Knessl and Joseph B. Keller.  Asymptotic behavior of high-order differences of the partition function.  Comm. Pure Appl. Math., 44(8-9):1033--1045, 1991. MR1127047
Charles Knessl.  On the diffusion approximation to two parallel queues with processor sharing.  IEEE Trans. Automat. Control, 36(12):1356--1367, 1991. MR1135650
C. Knessl and J. A. Morrison.  Heavy traffic analysis of the sojourn time in tandem queues with overtaking.  SIAM J. Appl. Math., 51(6):1740--1763, 1991. MR1136009
Charles Knessl.  On finite capacity processor-shared queues.  SIAM J. Appl. Math., 50(1):264--287, 1990. MR1036242
Charles Knessl and Joseph B. Keller.  Partition asymptotics from recursion equations.  SIAM J. Appl. Math., 50(2):323--338, 1990. MR1043589
Charles Knessl and Charles Tier.  Approximations to the moments of the sojourn time in a tandem queue with overtaking.  Comm. Statist. Stochastic Models, 6(3):499--524, 1990. MR1058351
C. Knessl, B. J. Matkowsky, Z. Schuss and C. Tier.  An integral equation approach to the $M/G/2$ queue.  Oper. Res., 38(3):506--518, 1990. MR1068283
Charles Knessl and Charles Tier.  Asymptotic expansions for large closed queuing networks.  J. Assoc. Comput. Mach., 37(1):144--174, 1990. MR1072432
Charles Knessl.  On the transient behavior of the $M/M/m/m$ loss model.  Comm. Statist. Stochastic Models, 6(4):749--776, 1990. MR1080420
Charles Knessl.  Refinements to heavy traffic limit theorems in queueing theory.  Oper. Res., 38(5):826--837, 1990. MR1095944
C. Knessl, B. J. Matkowsky, Z. Schuss and C. Tier.  Response times in processor-shared queues with state-dependent arrival rates.  Comm. Statist. Stochastic Models, 5(1):83--113, 1989. MR986588
C. Knessl, B. J. Matkowsky, Z. Schuss and C. Tier.  A state dependent $M/M/1$ queue: a production-inventory model.  Appl. Math. Lett., 1(3):235--239, 1988. MR963690
E. G. Coffman Jr., L. Flatto, I. Mitrani and C. Knessl.  Stochastic models of queue storage.  Probability in the Engineering and Information Sciences, 2:75-93, 1988.
W. L. Kath, C. Knessl and B. J. Matkowsky.  A variational approach to nonlinear singularly perturbed boundary-value problems.  Stud. Appl. Math., 77(1):61--88, 1987. MR1002282
C. Knessl, B. J. Matkowsky, Z. Schuss and C. Tier.  The two repairmen problem: a finite source $M/G/2$ queue.  SIAM J. Appl. Math., 47(2):367--397, 1987. MR881356
C. Knessl, B. J. Matkowsky, Z. Schuss and C. Tier.  Asymptotic expansions for a closed multiple access system.  SIAM J. Comput., 16(2):378--398, 1987. MR882538
C. Knessl, B. J. Matkowsky, Z. Schuss and C. Tier.  Distribution of the maximum buffer content during a busy period for state-dependent $M/G/1$ queues.  Comm. Statist. Stochastic Models, 3(2):191--226, 1987. MR903591
C. Knessl, B. J. Matkowsky, Z. Schuss and C. Tier.  Busy period distribution in state-dependent queues.  Queueing Systems Theory Appl., 2(3):285--305, 1987. MR925184
Charles Knessl, Bernard J. Matkowsky, Zeev Schuss and Charles Tier.  Two parallel $M/G/1$ queues where arrivals join the system with the smaller buffer content.  IEEE Trans. Comm., 35(11):1153--1158, 1987. MR977187
C. Knessl, B. J. Matkowsky, Z. Schuss and C. Tier.  A singular perturbation approach to first passage times for Markov jump processes.  J. Statist. Phys., 42(1-2):169--184, 1986. MR827880
C. Knessl, B. J. Matkowsky, Z. Schuss and C. Tier.  A finite capacity single-server queue with customer loss.  Comm. Statist. Stochastic Models, 2(1):97--121, 1986. MR836464
C. Knessl, B. J. Matkowsky, Z. Schuss and C. Tier.  Asymptotic analysis of a state-dependent $M/G/1$ queueing system.  SIAM J. Appl. Math., 46(3):483--505, 1986. MR841462
C. Knessl, B. J. Matkowsky, Z. Schuss and C. Tier.  On the performance of state-dependent single server queues.  SIAM J. Appl. Math., 46(4):657--697, 1986. MR849088
C. Knessl, B. J. Matkowsky, Z. Schuss and C. Tier.  System crash in a finite capacity $M/G/1$ queue.  Comm. Statist. Stochastic Models, 2(2):171--201, 1986. MR854152
C. Knessl, B. J. Matkowsky, Z. Schuss and C. Tier.  Boundary behavior of diffusion approximations to Markov jump processes.  J. Statist. Phys., 45(1-2):245--266, 1986. MR868206
Charles Knessl, Bernard J. Matkowsky, Zeev Schuss and Charles Tier.  Two parallel queues with dynamic routing.  IEEE Trans. Comm., 34(12):1170--1175, 1986. MR869742
C. Knessl, B. J. Matkowsky, Z. Schuss and C. Tier.  A Markov-modulated $M/G/1$ queue. I. Stationary distribution.  Queueing Systems Theory Appl., 1(4):355--374, 1986/87. MR899681
C. Knessl, B. J. Matkowsky, Z. Schuss and C. Tier.  A Markov-modulated $M/G/1$ queue. II. Busy period and time for buffer overflow.  Queueing Systems Theory Appl., 1(4):375--399, 1986/87. MR899682
C. Knessl, B. J. Matkowsky, Z. Schuss and C. Tier.  An asymptotic theory of large deviations for Markov jump processes.  SIAM J. Appl. Math., 45(6):1006--1028, 1985. MR813462
W. A. Doak, C. Knessl, H. Labaziewicz, S. E. O'Connor, L. Pup, G. Putz, M. Schranz, R. I. Walter, L. Yang and N. H. Werstiuk.  The preparation of specifically deuterated diphenylamines.  Canadian Journal of Chemistry, 63(12):3371--3373, 1985.
B. J. Matkowsky, Z. Schuss, C. Knessl, C. Tier and M. Mangel.  Asymptotic solution of the Kramers-Moyal equation and first-passage times for Markov jump processes.  Phys. Rev. A (3), 29(6):3359--3369, 1984. MR747593
B. J. Matkowsky, Z. Schuss, C. Knessl, C. Tier and M. Mangel.  First passage times for processes governed by master equations.  In Fluctuations and sensitivity in nonequilibrium systems (Austin, Tex., 1984), pages 19--36.  Springer, Berlin, 1984. MR771131
C. Knessl, M. Mangel, B. J. Matkowsky, Z. Schuss and C. Tier.  Solutions of Kramers-Moyal equations for problems in chemical physics.  J. Chem. Phys., 81(3):1285--1293, 1984.
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