Zhen, Qiang; van Leeuwaarden, Johan S. H.; Knessl, Charles On the sojourn time distribution in a finite population Markovian processor sharing queue. (English) Zbl 1401.60170 IMA J. Appl. Math. 82, No. 1, 33-59 (2017). MSC: 60K25 68M20 90B22 PDFBibTeX XMLCite \textit{Q. Zhen} et al., IMA J. Appl. Math. 82, No. 1, 33--59 (2017; Zbl 1401.60170) Full Text: DOI arXiv
Zhen, Qiang; Knessl, Charles Asymptotic analysis of spectral properties of finite capacity processor shared queues. (English) Zbl 1418.34157 Stud. Appl. Math. 131, No. 2, 179-210 (2013). MSC: 34L10 34L15 34E10 PDFBibTeX XMLCite \textit{Q. Zhen} and \textit{C. Knessl}, Stud. Appl. Math. 131, No. 2, 179--210 (2013; Zbl 1418.34157) Full Text: DOI arXiv
Tan, Xiaoqian; Knessl, Charles; Yang, Yongzhi (Peter) On finite capacity queues with time dependent arrival rates. (English) Zbl 1295.60104 Stochastic Processes Appl. 123, No. 6, 2175-2227 (2013). MSC: 60K25 90B22 PDFBibTeX XMLCite \textit{X. Tan} et al., Stochastic Processes Appl. 123, No. 6, 2175--2227 (2013; Zbl 1295.60104) Full Text: DOI
Zhen, Qiang; Knessl, Charles On spectral properties of finite population processor shared queues. (English) Zbl 1278.90107 Math. Methods Oper. Res. 77, No. 2, 147-176 (2013). MSC: 90B22 68M20 PDFBibTeX XMLCite \textit{Q. Zhen} and \textit{C. Knessl}, Math. Methods Oper. Res. 77, No. 2, 147--176 (2013; Zbl 1278.90107) Full Text: DOI arXiv
Zhen, Qiang; Knessl, Charles An explicit solution to the chessboard pebbling problem. (English) Zbl 1260.05030 J. Difference Equ. Appl. 19, No. 2, 201-208 (2013). MSC: 05B30 05A15 PDFBibTeX XMLCite \textit{Q. Zhen} and \textit{C. Knessl}, J. Difference Equ. Appl. 19, No. 2, 201--208 (2013; Zbl 1260.05030) Full Text: DOI arXiv
Dominici, Diego; Knessl, Charles Asymptotic analysis of a family of polynomials associated with the inverse error function. (English) Zbl 1259.34047 Rocky Mt. J. Math. 42, No. 3, 847-872 (2012). Reviewer: Alberto Lastra Sedano (Burgos) MSC: 34E20 33E30 34E10 34A30 PDFBibTeX XMLCite \textit{D. Dominici} and \textit{C. Knessl}, Rocky Mt. J. Math. 42, No. 3, 847--872 (2012; Zbl 1259.34047) Full Text: DOI arXiv Euclid
Sohn, Eunju; Knessl, Charles Some exact and asymptotic solutions to single server models of dynamic storage. (English) Zbl 1246.90013 Stoch. Models 28, No. 2, 248-280 (2012). MSC: 90B05 90B22 60K25 34E10 PDFBibTeX XMLCite \textit{E. Sohn} and \textit{C. Knessl}, Stoch. Models 28, No. 2, 248--280 (2012; Zbl 1246.90013) Full Text: DOI
Xu, Miao; Knessl, Charles On a free boundary problem for an American put option under the CEV process. (English) Zbl 1211.91242 Appl. Math. Lett. 24, No. 7, 1191-1198 (2011). MSC: 91G20 91G80 PDFBibTeX XMLCite \textit{M. Xu} and \textit{C. Knessl}, Appl. Math. Lett. 24, No. 7, 1191--1198 (2011; Zbl 1211.91242) Full Text: DOI arXiv
Zhen, Qiang; van Leeuwaarden, Johan S. H.; Knessl, Charles On a processor sharing queue that models balking. (English) Zbl 1203.93153 Math. Methods Oper. Res. 72, No. 3, 453-476 (2010). MSC: 93C85 93E03 68M20 PDFBibTeX XMLCite \textit{Q. Zhen} et al., Math. Methods Oper. Res. 72, No. 3, 453--476 (2010; Zbl 1203.93153) Full Text: DOI arXiv
Sohn, Eunju; Knessl, Charles Storage allocation under processor sharing. I: Exact solutions and asymptotics. (English) Zbl 1187.90103 Queueing Syst. 65, No. 1, 1-18 (2010). MSC: 90B22 68M20 PDFBibTeX XMLCite \textit{E. Sohn} and \textit{C. Knessl}, Queueing Syst. 65, No. 1, 1--18 (2010; Zbl 1187.90103) Full Text: DOI arXiv
Zhen, Qiang; Knessl, Charles Asymptotic expansions for the sojourn time distribution in the \(M/G/1\)-PS queue. (English) Zbl 1189.93132 Math. Methods Oper. Res. 71, No. 2, 201-244 (2010). MSC: 93E03 60K25 93C83 PDFBibTeX XMLCite \textit{Q. Zhen} and \textit{C. Knessl}, Math. Methods Oper. Res. 71, No. 2, 201--244 (2010; Zbl 1189.93132) Full Text: DOI arXiv
Lynch, Sean; Knessl, Charles Drift-diffusion past a circle: shadow region asymptotics. (English) Zbl 1188.41024 SIAM J. Appl. Math. 69, No. 6, 1559-1579 (2009). Reviewer: José L. Lopez (Pamplona) MSC: 41A60 35J25 33C10 PDFBibTeX XMLCite \textit{S. Lynch} and \textit{C. Knessl}, SIAM J. Appl. Math. 69, No. 6, 1559--1579 (2009; Zbl 1188.41024) Full Text: DOI
Knessl, Charles; Morrison, John A. A two-dimensional diffusion approximation for a loss model with trunk reservation. (English) Zbl 1181.60140 SIAM J. Appl. Math. 69, No. 5, 1457-1476 (2009). Reviewer: János Sztrik (Debrecen) MSC: 60K30 90B22 68M20 PDFBibTeX XMLCite \textit{C. Knessl} and \textit{J. A. Morrison}, SIAM J. Appl. Math. 69, No. 5, 1457--1476 (2009; Zbl 1181.60140) Full Text: DOI
Knessl, Charles; Dominici, Diego Ernesto Asymptotic analysis of a fluid model modulated by an M/M/1 queue. (English) Zbl 1155.60041 Adv. Appl. Probab. 40, No. 3, 856-881 (2008). Reviewer: János Sztrik (Debrecen) MSC: 60K25 60J25 34E10 PDFBibTeX XMLCite \textit{C. Knessl} and \textit{D. E. Dominici}, Adv. Appl. Probab. 40, No. 3, 856--881 (2008; Zbl 1155.60041) Full Text: DOI arXiv
Knessl, Charles On the number of reachable configurations for the chessboard pebbling problem. (English) Zbl 1147.05004 Math. Comput. Modelling 47, No. 1-2, 127-139 (2008). MSC: 05A15 PDFBibTeX XMLCite \textit{C. Knessl}, Math. Comput. Modelling 47, No. 1--2, 127--139 (2008; Zbl 1147.05004) Full Text: DOI
Yao, Haishen; Knessl, Charles Some first passage time problems for the shortest queue model. (English) Zbl 1134.60412 Queueing Syst. 58, No. 2, 105-119 (2008). MSC: 60K25 90B22 41A60 PDFBibTeX XMLCite \textit{H. Yao} and \textit{C. Knessl}, Queueing Syst. 58, No. 2, 105--119 (2008; Zbl 1134.60412) Full Text: DOI
Dominici, Diego; Knessl, Charles Ray solution of singularly perturbed elliptic PDE with applications to communications networks. (English) Zbl 1114.35057 SIAM J. Appl. Math. 66, No. 6, 1871-1894 (2006). MSC: 35J25 35C20 34E20 60K25 94A05 PDFBibTeX XMLCite \textit{D. Dominici} and \textit{C. Knessl}, SIAM J. Appl. Math. 66, No. 6, 1871--1894 (2006; Zbl 1114.35057) Full Text: DOI arXiv
Knessl, Charles; Yang, Yongzhi Peter On the Erlang loss model with time dependent input. (English) Zbl 1142.60402 Queueing Syst. 52, No. 1, 49-104 (2006). MSC: 60K25 34E10 90B22 PDFBibTeX XMLCite \textit{C. Knessl} and \textit{Y. P. Yang}, Queueing Syst. 52, No. 1, 49--104 (2006; Zbl 1142.60402) Full Text: DOI
Knessl, Charles; Morrison, John A. Blocking probabilities for an underloaded or overloaded link with trunk reservation. (English) Zbl 1091.94002 SIAM J. Appl. Math. 66, No. 1, 82-97 (2005). MSC: 94A05 60K25 90B18 PDFBibTeX XMLCite \textit{C. Knessl} and \textit{J. A. Morrison}, SIAM J. Appl. Math. 66, No. 1, 82--97 (2005; Zbl 1091.94002) Full Text: DOI
Knessl, Charles Numerical studies of the asymptotic height distribution in binary search trees. (English) Zbl 1035.68041 Discrete Math. Theor. Comput. Sci. 6, No. 1, 91-100 (2003). MSC: 68P10 68R10 PDFBibTeX XMLCite \textit{C. Knessl}, Discrete Math. Theor. Comput. Sci. 6, No. 1, 91--100 (2003; Zbl 1035.68041) Full Text: EuDML EMIS
Knessl, Charles; Morrison, John A. Heavy traffic analysis of two coupled processors. (English) Zbl 1013.90046 Queueing Syst. 43, No. 3, 173-220 (2003). MSC: 90B22 PDFBibTeX XMLCite \textit{C. Knessl} and \textit{J. A. Morrison}, Queueing Syst. 43, No. 3, 173--220 (2003; Zbl 1013.90046) Full Text: DOI
Knessl, Charles; Szpankowski, Wojciech The height of a binary search tree: the limiting distribution perspective. (English) Zbl 1061.68039 Theor. Comput. Sci. 289, No. 1, 649-703 (2002). MSC: 68P10 68P05 PDFBibTeX XMLCite \textit{C. Knessl} and \textit{W. Szpankowski}, Theor. Comput. Sci. 289, No. 1, 649--703 (2002; Zbl 1061.68039) Full Text: DOI
Knessl, Charles On two-dimensional convection-diffusion past a circle. (English) Zbl 1103.35319 SIAM J. Appl. Math. 62, No. 1, 310-335 (2001). MSC: 35J25 33C10 35C10 PDFBibTeX XMLCite \textit{C. Knessl}, SIAM J. Appl. Math. 62, No. 1, 310--335 (2001; Zbl 1103.35319) Full Text: DOI
Knessl, Charles; Yang, Yongzhi Analysis of a Brownian particle moving in a time-dependent drift field. (English) Zbl 1012.60073 Asymptotic Anal. 27, No. 3-4, 281-319 (2001). Reviewer: Ion Cuculescu (Bucureşti) MSC: 60J65 35C05 35C20 PDFBibTeX XMLCite \textit{C. Knessl} and \textit{Y. Yang}, Asymptotic Anal. 27, No. 3--4, 281--319 (2001; Zbl 1012.60073)
Knessl, C. Geometrical optics and chessboard pebbling. (English) Zbl 0968.05007 Appl. Math. Lett. 14, No. 3, 365-373 (2001). Reviewer: Péter L.Erdős (Budapest) MSC: 05A16 05A15 11B37 PDFBibTeX XMLCite \textit{C. Knessl}, Appl. Math. Lett. 14, No. 3, 365--373 (2001; Zbl 0968.05007) Full Text: DOI
Knessl, Charles; Szpankowski, Wojciech Asymptotic behavior of the height in a digital search tree and the longest phrase of the Lempel–Ziv scheme. (English) Zbl 0968.68067 SIAM J. Comput. 30, No. 3, 923-964 (2000). MSC: 68Q25 68P05 PDFBibTeX XMLCite \textit{C. Knessl} and \textit{W. Szpankowski}, SIAM J. Comput. 30, No. 3, 923--964 (2000; Zbl 0968.68067) Full Text: DOI
Knessl, Charles Asymptotic analysis of a backward-forward parabolic problem for data-handling systems. (English) Zbl 0979.60086 SIAM J. Appl. Math. 61, No. 3, 914-933 (2000). Reviewer: C.Rainer MSC: 60K25 35K20 35B40 PDFBibTeX XMLCite \textit{C. Knessl}, SIAM J. Appl. Math. 61, No. 3, 914--933 (2000; Zbl 0979.60086) Full Text: DOI
Knessl, Charles; Tier, Charles A diffusion model for two tandem queues with general renewal input. (English) Zbl 0930.60084 Commun. Stat., Stochastic Models 15, No. 2, 299-343 (1999). Reviewer: D.N.Shanbhag (Sheffield) MSC: 60K25 90B22 PDFBibTeX XMLCite \textit{C. Knessl} and \textit{C. Tier}, Commun. Stat., Stochastic Models 15, No. 2, 299--343 (1999; Zbl 0930.60084) Full Text: DOI
Knessl, Charles; Tier, Charles Heavy traffic analysis of a Markov-modulated queue with finite capacity and general service times. (English) Zbl 0915.60082 SIAM J. Appl. Math. 58, No. 1, 257-323 (1998). Reviewer: E.A.van Doorn (Enschede) MSC: 60K25 34E20 PDFBibTeX XMLCite \textit{C. Knessl} and \textit{C. Tier}, SIAM J. Appl. Math. 58, No. 1, 257--323 (1998; Zbl 0915.60082) Full Text: DOI
Tan, Xiaoqian; Knessl, Charles Integral representations and asymptotics for infinite- and finite-capacity queues described by the unfinished work. I. (English) Zbl 0874.60086 SIAM J. Appl. Math. 57, No. 3, 791-823 (1997). MSC: 60K30 34E20 PDFBibTeX XMLCite \textit{X. Tan} and \textit{C. Knessl}, SIAM J. Appl. Math. 57, No. 3, 791--823 (1997; Zbl 0874.60086) Full Text: DOI
Tan, Xiaoming; Knessl, Charles A fork-join queueing model: Diffusion approximation, integral representations and asymptotics. (English) Zbl 0860.60078 Queueing Syst. 22, No. 3-4, 287-322 (1996). MSC: 60K25 90B22 PDFBibTeX XMLCite \textit{X. Tan} and \textit{C. Knessl}, Queueing Syst. 22, No. 3--4, 287--322 (1996; Zbl 0860.60078) Full Text: DOI
Knessl, Charles; Peters, Craig Steven Exact and asymptotic solutions for the time-dependent problem of collective ruin. II. (English) Zbl 0879.60104 SIAM J. Appl. Math. 56, No. 5, 1471-1521 (1996). MSC: 60K30 34E20 PDFBibTeX XMLCite \textit{C. Knessl} and \textit{C. S. Peters}, SIAM J. Appl. Math. 56, No. 5, 1471--1521 (1996; Zbl 0879.60104) Full Text: DOI
Knessl, Charles; Tier, Charles Mean time for the development of large workloads and large queue lengths in the GI/G/1 queue. (English) Zbl 0858.60080 J. Appl. Math. Stochastic Anal. 9, No. 2, 107-142 (1996). MSC: 60K25 34E15 PDFBibTeX XMLCite \textit{C. Knessl} and \textit{C. Tier}, J. Appl. Math. Stochastic Anal. 9, No. 2, 107--142 (1996; Zbl 0858.60080) Full Text: DOI EuDML
Tan, Xiaoming; Knessl, Charles Heavy traffic asymptotics for a gated, infinite-server queue with uniform service times. (English) Zbl 0815.60095 SIAM J. Appl. Math. 54, No. 6, 1768-1779 (1994). Reviewer: E.A.van Doorn (Enschede) MSC: 60K25 60K30 34E20 PDFBibTeX XMLCite \textit{X. Tan} and \textit{C. Knessl}, SIAM J. Appl. Math. 54, No. 6, 1768--1779 (1994; Zbl 0815.60095) Full Text: DOI
Knessl, Charles; Peters, Craig Steven Exact and asymptotic solutions for the time-dependent problem of collective ruin. I. (English) Zbl 0811.60088 SIAM J. Appl. Math. 54, No. 6, 1745-1767 (1994). MSC: 60K30 34E20 PDFBibTeX XMLCite \textit{C. Knessl} and \textit{C. S. Peters}, SIAM J. Appl. Math. 54, No. 6, 1745--1767 (1994; Zbl 0811.60088) Full Text: DOI
Knessl, Charles On the sojourn time distribution in a finite capacity processor shared queue. (English) Zbl 0795.68020 J. Assoc. Comput. Mach. 40, No. 5, 1238-1301 (1993). MSC: 68M20 60K25 PDFBibTeX XMLCite \textit{C. Knessl}, J. Assoc. Comput. Mach. 40, No. 5, 1238--1301 (1993; Zbl 0795.68020) Full Text: DOI
Xie, Shisheng; Knessl, Charles On the transient behavior of the Erlang loss model: Heavy usage asymptotics. (English) Zbl 0776.60118 SIAM J. Appl. Math. 53, No. 2, 555-599 (1993). Reviewer: V.Cohen (Chaumont-en-Vexin) MSC: 60K30 34E20 PDFBibTeX XMLCite \textit{S. Xie} and \textit{C. Knessl}, SIAM J. Appl. Math. 53, No. 2, 555--599 (1993; Zbl 0776.60118) Full Text: DOI
Tan, Xiaoming; Knessl, Charles A finite capacity PS queue which models switching times. (English) Zbl 0776.60117 SIAM J. Appl. Math. 53, No. 2, 491-554 (1993). Reviewer: V.Cohen (Chaumont-en-Vexin) MSC: 60K30 34E20 PDFBibTeX XMLCite \textit{X. Tan} and \textit{C. Knessl}, SIAM J. Appl. Math. 53, No. 2, 491--554 (1993; Zbl 0776.60117) Full Text: DOI
Knessl, Charles; Keller, Joseph B. Asymptotic properties of eigenvalues of integral equations. (English) Zbl 0725.45001 SIAM J. Appl. Math. 51, No. 1, 214-232 (1991). Reviewer: V.C.Boffi (Roma) MSC: 45C05 45M05 45L05 PDFBibTeX XMLCite \textit{C. Knessl} and \textit{J. B. Keller}, SIAM J. Appl. Math. 51, No. 1, 214--232 (1991; Zbl 0725.45001) Full Text: DOI
Knessl, Charles; Tier, Charles Asymptotic expansions for large closed queueing networks. (English) Zbl 0698.68036 J. Assoc. Comput. Mach. 37, No. 1, 144-174 (1990). MSC: 68M20 68N25 60K25 90B22 PDFBibTeX XMLCite \textit{C. Knessl} and \textit{C. Tier}, J. Assoc. Comput. Mach. 37, No. 1, 144--174 (1990; Zbl 0698.68036) Full Text: DOI