Optimal design and control of queues

We have divided this review into two parts. The first part is concerned with the optimal design of queueing systems and the second part deals with the optimal control of queueing systems. The second part, which has the lion’s share of the review since it has received the most attention, focuses mainly on the modelling aspects of the problem and describes the different kinds of threshold (control) policy models available in the literature. To limit the scope of this survey, we decided to limit ourselves to research on papers dealing with the three policies (N, T, and D), where a cost function is designed specifically and optimal thresholds that yield minimum cost are sought.

[1]  Jeyaveerasingam George Shanthikumar.  ANALYSIS OF THE CONTROL OF QUEUES WITH SHORTEST PROCESSING TIME SERVICE DISCIPLINE , 1980 .

[2]  Eugene A. Feinberg,et al.  Optimal Switching Policies for M/G/1 Queues with Two Performance Criteria , 1995 .

[3]  Colin E. Bell,et al.  Characterization and Computation of Optimal Policies for Operating an M/G/1 Queuing System with Removable Server , 1971, Oper. Res..

[4]  Tadashi Dohi,et al.  Optimal Timing Strategies for Controlled M/G/1 Queueing System via Diffusion Approximation Approach , 1997 .

[5]  Jesús R. Artalejo,et al.  Accessible bibliography on retrial queues , 1999 .

[6]  L. Tadj,et al.  A Quorum Queueing System with a Random Setup Time under N-policy and with Bernoulli Vacation Schedule , 2006 .

[7]  Peter Köchel,et al.  Finite queueing systems--structural investigations and optimal design , 2004 .

[8]  L. Tadj,et al.  A bulk quorum queueing system with a random setup time under N-policy and with Bernoulli vacation schedule , 2006 .

[9]  A.J.J. Talman,et al.  A simple proof of the optimality of the best N‐policy in the M/G/l queueing control problem with removable server , 1979 .

[10]  Mandyam M. Srinivasan,et al.  Random review production/inventory systems with compound Poisson demands and arbitrary processing times , 1991 .

[11]  Colin E. Bell.  Optimal Operation of an M/M/2 Queue with Removable Servers , 1980, Oper. Res..

[12]  Jesús R. Artalejo,et al.  On the M/G/1 queue with D-policy , 2001 .

[13]  Warren B. Powell,et al.  The Bulk Service Queue with a General Control Strategy: Theoretical Analysis and a New Computational Procedure , 1986, Oper. Res..

[14]  Attahiru Sule Alfa,et al.  Discrete NT-policy single server queue with Markovian arrival process and phase type service , 1996 .

[15]  Jau-Chuan Ke,et al.  The optimal control of an M/G/1 queueing system with server vacations, startup and breakdowns , 2003 .

[16]  Howard J. Weiss.  The Computation of Optimal Control Limits for a Queue with Batch Services , 1979 .

[17]  Peter Kolesar,et al.  Multilevel Bulk Service Queues , 1972, Oper. Res..

[18]  Vidyadhar G. Kulkarni,et al.  Retrial queues revisited , 1998 .

[19]  Jesús R. Artalejo,et al.  A classified bibliography of research on retrial queues: Progress in 1990–1999 , 1999 .

[20]  Toshikazu Kimura,et al.  Optimal control of an M/G/1 queuing system with removable server via diffusion approximation , 1981 .

[21]  Kuo-Hsiung Wang.  Optimal control of an M/Ek/1 queueing system with removable service station subject to breakdowns , 1997 .

[22]  Attahiru Sule Alfa,et al.  Optimal policies for M/M/m queue with two different kinds of (N, T)-policies , 2000 .

[23]  J. Moder,et al.  Queuing With Fixed and Variable Channels , 1962 .

[24]  K. C. So,et al.  Optimality of threshold policies in single-server queueing systems with server vacations , 1991, Advances in Applied Probability.

[25]  Jesus R. Artalejo,et al.  A note on the optimality of the N- and D-policies for the M/G/1 queue , 2002, Oper. Res. Lett..

[26]  Ammar M. Sarhan,et al.  Effect of the server capacity distribution on the optimal control of a bulk service queueing system , 2003 .

[27]  Jewgeni H. Dshalalow.  Queueing processes in bulk systems under the D-policy , 1998 .

[28]  Ravi P. Agarwal,et al.  New fluctuation analysis of D-policy bulk queues with multiple vacations , 2005, Math. Comput. Model..

[29]  Song-Kyoo Kim,et al.  Stochastic disaster recovery systems with external resources , 2002 .

[30]  Kyung C. Chae,et al.  Operating characteristics of MX/G/1 queue with N-policy , 1994, Queueing Syst. Theory Appl..

[31]  Richard Stern.  Seoul, Korea , 1998 .

[32]  Wayne L. Winston,et al.  Technical Note—Optimality of Monotonic Policies for Multiple-Server Exponential Queuing Systems with State-Dependent Arrival Rates , 1978 .

[33]  Eitan Altman,et al.  Optimality of a Threshold Policy in theM/M/ queue with repeated vacations , 1996, Math. Methods Oper. Res..

[34]  Micha Yadin,et al.  On queueing systems with variable service capacities , 1967 .

[35]  Mandyam M. Srinivasan,et al.  Control policies for the M X /g/ 1 queueing system , 1989 .

[36]  Kyung C. Chae,et al.  Batch arrival queue with N-policy and single vacation , 1995, Comput. Oper. Res..

[37]  Kuo-Hsiung Wang,et al.  (Applied Mathematical Modelling,23(8):651-666)Optimal Control of a Removable and Non-reliable Server in an Infinite and a Finite M/H2/1 Queueing System , 1999 .

[38]  Shaler Stidham,et al.  Optimal Control of Queueing Systems , 1974 .

[39]  R. Serfozo,et al.  Optimal control of batch service queues , 1973, Advances in Applied Probability.

[40]  B. T. Doshi,et al.  Queueing systems with vacations — A survey , 1986, Queueing Syst. Theory Appl..

[41]  Alexander N. Dudin.  Optimal Control for an Mx/G/1 Queue with Two Operation Modes , 1997 .

[42]  O. J. Boxma,et al.  Note---Note on a Control Problem of Balachandran and Tijms , 1976 .

[43]  Jewgeni H. Dshalalow.  On applications of excess level processes to ( N , D ) -policy bulk queueing systems , 1996 .

[44]  Jung Woo Baek,et al.  Analysis of the M X /G/1 Queue Under D-Policy , 2005 .

[45]  P. Patrick Wang.  Markovian queueing models with periodic-review , 1996, Comput. Oper. Res..

[46]  Wen Lea Pearn,et al.  Optimal Management Policy for Heterogeneous Arrival Queueing Systems with Server Breakdowns and Vacations , 2004 .

[47]  Jesus R. Artalejo,et al.  Analysis of an M/G/1 queue with constant repeated attempts and server vacations , 1997, Comput. Oper. Res..

[48]  Tetsuya Takine,et al.  MAP/G/1 QUEUES UNDER N-POLICY WITH AND WITHOUT VACATIONS , 1996 .

[49]  A. Krishnamoorthy,et al.  Modified N-policy for M/G/1 queues , 2002, Comput. Oper. Res..

[50]  Lotfi Tadj,et al.  On an M/G/1 quorum queueing system under T-policy , 2003, J. Oper. Res. Soc..

[51]  M. Yadin,et al.  Queueing Systems with a Removable Service Station , 1963 .

[52]  C. Liao.  Optimal release time on a stochastic single machine , 1992 .

[53]  Hyo-Seong Lee.  Optimal control of the MX/G/1/K queue with multiple server vacations , 1995, Comput. Oper. Res..

[54]  Kyung C. Chae,et al.  Workload and Waiting Time Analyses of MAP/G/1 Queue under D-policy , 2004, Queueing Syst. Theory Appl..

[55]  Jau-Chuan Ke.  The optimal control of an M/G/1 queueing system with server startup and two vacation types , 2003 .

[56]  James G. C. Templeton,et al.  A survey on retrial queues , 1989 .

[57]  José Romaní,et al.  Un modelo de la teoria de colas con numero variable de canales , 1957 .

[58]  No Ik Park,et al.  DECOMPOSITIONS OF THE QUEUE LENGTH DISTRIBUTIONS IN THE MAP/G/1 QUEUE UNDER MULTIPLE AND SINGLE VACATIONS WITH N-POLICY , 2001 .

[59]  Shaler Stidham,et al.  On the Optimality of Single-Server Queuing Systems , 1970, Oper. Res..

[60]  J. Medhi.  Single Server Queueing System with Poisson Input: A Review of Some Recent Developments , 1997 .

[61]  Jau-Chuan Ke.  The control policy of an M[x]/G/1 queueing system with server startup and two vacation types , 2001, Math. Methods Oper. Res..

[62]  Panagiotis Kasteridis,et al.  On the d-policy for the m/g/1 queue , 2001 .

[63]  Matthew Rosenshine,et al.  Scheduling arrivals to queues , 1990, Comput. Oper. Res..

[64]  Jacques Teghem.  Optimal control of a removable server in an M/G/1 queue with finite capacity , 1987 .

[65]  Zhe George Zhang,et al.  Optimal Two-Threshold Policies in an M/G/1 Queue With Two Vacation Types , 1997, Perform. Evaluation.

[66]  Ho Woo Lee,et al.  Start‐up class models in multiple‐class queues with N‐policy , 1999, Queueing Syst. Theory Appl..

[67]  Xin Chen,et al.  Optimal service rates for the state-dependent M/G/1 queues in steady state , 2001, Oper. Res. Lett..

[68]  Samuli Aalto.  Optimal control of batch service queues with compound Poisson arrivals and finite service capacity , 1998, Math. Methods Oper. Res..

[69]  Gautam Choudhury,et al.  THE STOCHASTIC DECOMPOSITION RESULTS OF BATCH ARRIVAL POISSON QUEUE WITH A GRAND VACATION PROCESS , 2000 .

[70]  B. D. Sivazlian.  Approximate Optimal Solution for a D-Policy in an M/G/X Queuing System , 1979 .

[71]  Jau-Chuan Ke,et al.  Control policy of a hysteretic bulk queueing system , 2005, Math. Comput. Model..

[72]  Kashi R. Balachandran,et al.  Control Policies for a Single Server System , 1973 .

[73]  Carl M. Harris,et al.  Fundamentals of queueing theory , 1975 .

[74]  Vladimir Rykov,et al.  Optimal Control of Queueing Systems with Heterogeneous Servers , 2004, Queueing Syst. Theory Appl..

[75]  Wen Lea Pearn,et al.  Sensitivity analysis of the optimal management policy for a queuing system with a removable and non-reliable server , 2004, Comput. Ind. Eng..

[76]  Gautam Choudhury,et al.  A batch arrival queue with an additional service channel under N-policy , 2004, Appl. Math. Comput..

[77]  No Ik Park,et al.  Using Factorization for Waiting Times in BMAP/G/1 Queues with N-Policy and Vacations , 2004 .

[78]  Frederick S. Hillier,et al.  Economic Models for Industrial Waiting Line Problems , 1963 .

[79]  Kuo-Hsiung Wang,et al.  Optimal control of a removable and non-reliable server in a markovian queueing system with finite capacity , 1995 .

[80]  Jesús R. Artalejo,et al.  Standard and retrial queueing systems: a comparative analysis , 2002 .

[81]  Matthew J. Sobel.  Optimal Operation of Queues , 1974 .

[82]  R. Nadarajan,et al.  Analysis of a bulk queue with N-policy multiple vacations and setup times , 1998, Comput. Oper. Res..

[83]  Michael J. Magazine,et al.  A Classified Bibliography of Research on Optimal Design and Control of Queues , 1977, Oper. Res..

[84]  Rein D. Nobel,et al.  Optimal control of a queueing system with heterogeneous servers and setup costs , 2000, IEEE Trans. Autom. Control..

[85]  Offer Kella.  Optimal Control of the Vacation Scheme in an M/G/1 Queue , 1990, Oper. Res..

[86]  Offer Kella.  The threshold policy in the M/G/1 queue with server vacations , 1989 .

[87]  Kneale T. Marshall,et al.  Bounds on the Optimal Operating Policy for a Class of Single-Server Queues , 1968, Oper. Res..

[88]  Kashi R. Balachandran.  Queue Length Dependent Priority Queues , 1971 .

[89]  Charles E. Skinner,et al.  A Priority Queuing System with Server-Walking Time , 1967, Oper. Res..

[90]  Rein D. Nobel,et al.  Optimal control for an MX/G/1 queue with two service modes , 1999, Eur. J. Oper. Res..

[91]  K. Chae,et al.  MX/G/1 Vacation Models with N-Policy: Heuristic Interpretation of the Mean Waiting Time , 1995 .

[92]  Kuo-Hsiung Wang,et al.  Cost analysis of the M/M/R machine repair problem with balking, reneging, and server breakdowns , 1999, J. Oper. Res. Soc..

[93]  Marvin Hersh,et al.  The optimal strategy structure of an intermittently operated service channel , 1980 .

[94]  Jacques Teghem,et al.  Control of the service process in a queueing system , 1986 .

[95]  Kambiz Farahmand,et al.  Single line queue with repeated demands , 1990, Queueing Syst. Theory Appl..

[96]  Zhe George Zhang,et al.  The Threshold Policy In An M/G/1 Queue With An Exceptional First Vacation , 1998 .

[97]  Georges Brigham.  On a Congestion Problem in an Aircraft Factory , 1955, Oper. Res..

[98]  Kailash C. Madan,et al.  A two-stage batch arrival queueing system with a modified bernoulli schedule vacation under N-policy , 2005, Math. Comput. Model..

[99]  Daniel P. Heyman,et al.  Optimal Operating Policies for M/G/1 Queuing Systems , 1968, Oper. Res..

[100]  Offer Kella,et al.  Optimality of D-Policies for an M/G/1 Queue with a Removable Server , 2002, Queueing Syst. Theory Appl..

[101]  J. George Shanthikumar,et al.  M/G/1 Queues with Scheduling within Generations and Removable Server , 1981, Oper. Res..

[102]  Joseph D. Blackburn.  Optimal Control of a Single-Server Queue with Balking and Reneging , 1972 .

[103]  Daniel P. Heyman,et al.  The T-Policy for the M/G/1 Queue , 1977 .

[104]  Jesus R. Artalejo,et al.  Performance analysis and optimal control of the Geo/Geo/c queue , 2003, Perform. Evaluation.

[105]  Shokri Z. Selim.  Time-dependent solution and optimal control of a bulk service queue , 1997 .

[106]  K. H. Wang,et al.  Optimal Control of an M/Ek/1 Queueing System with a Removable Service Station , 1995 .

[107]  Sun Hur,et al.  An Analysis of M/G/1 System with N and T-Policy , 2003 .

[108]  Diego Klabjan,et al.  The complexity of cover inequality separation , 1998, Oper. Res. Lett..

[109]  U. Yechiali,et al.  Utilization of idle time in an M/G/1 queueing system Management Science 22 , 1975 .

[110]  Philip M. Morse,et al.  Queues, Inventories, And Maintenance , 1958 .

[111]  J. R. Artalejo,et al.  Analysis of an M/G/1 queue with two types of impatient units , 1995, Advances in Applied Probability.

[112]  Percy H. Brill,et al.  An exponential queue with competition for service , 2000, Eur. J. Oper. Res..

[113]  U. Narayan Bhat,et al.  A Statistical Technique for the Control of Traffic Intensity in the Queuing Systems M/G/1 and GI/M/1 , 1972, Oper. Res..

[114]  Howard J. Weiss.  Technical Note - Further Results on an Infinite Capacity Shuttle with Control at a Single Terminal , 1981, Oper. Res..

[115]  Jau-Chuan Ke,et al.  Control policy of a hysteretic queueing system , 2003, Math. Methods Oper. Res..

[116]  P. V. Ushakumari,et al.  A queueing system with single arrival bulk service and single departure , 2000 .

[117]  Lotfi Tadj,et al.  A quorum queueing system under D-policy , 2003, Appl. Math. Comput..

[118]  R. Bellman.  Dynamic programming. , 1957, Science.

[119]  Jung Woo Baek,et al.  BMAP/G/1 Queue Under D-Policy: Queue Length Analysis , 2005 .

[120]  Rosa E. Lillo,et al.  On optimal exhaustive policies for the M/G/1-queue , 2000, Oper. Res. Lett..

[121]  Matthew J. Sobel,et al.  Optimal Average-Cost Policy for a Queue with Start-Up and Shut-Down Costs , 1969, Oper. Res..

[122]  E. Feinberg,et al.  Bicriterion Optimization of an M/G/1 Queue with A Removable Server , 1996 .

[123]  Shaler Stidham.  Optimal control of stochastic service systems , 1978 .

[124]  Chakib Tadj,et al.  On an M/D/1 queueing system , 2003 .

[125]  Richard F. Gebhard.  A queuing process with bilevel hysteretic service‐rate control , 1967 .

[126]  Kenneth R. Baker,et al.  A Note On Operating Policies For The Queue M/M/1 With Exponential Startups , 1973 .

[127]  Nobuko Igaki.  Exponential two server queue withN-policy and general vacations , 1992, Queueing Syst. Theory Appl..

[128]  Ho Woo Lee,et al.  ANALYSIS OF THE M(X)/G/1 QUEUE WITH N-POLICY AND MULTIPLE VACATIONS , 1994 .

[129]  Wen Lea Pearn,et al.  Optimal management of the N-policy M/Ek/1 queuing system with a removable service station: a sensitivity investigation , 2004, Comput. Oper. Res..

[130]  Raymond G. Vickson,et al.  The Optimal Service Policies In An M/G/1 Queueing System With Multiple Vacation Types , 2001 .

[131]  Ho Woo Lee,et al.  Optimal strategy in N-policy production system with early set-up , 1997 .

[132]  Samuli Aalto.  Optimal control of batch service queues with finite service capacity and linear holding costs , 2000, Math. Methods Oper. Res..

[133]  J. Medhi,et al.  Poisson input queueing system with startup time and under control-operating policy , 1987, Comput. Oper. Res..

[134]  Gautam Choudhury.  An M/G/1 queueing system with two phase service under D-policy , 2005 .

[135]  T. B. Crabill.  Optimal Control of a Service Facility with Variable Exponential Service Times and Constant Arrival Rate , 1972 .

[136]  Shunji Osaki,et al.  Optimal policies for a controlled queueing system with removable server under a random vacation circumstance , 2000 .

[137]  Kuo-Hsiung Wang,et al.  Optimal control of an M/M/2 queueing system with finite capacity operating under the triadic (0,Q,N,M) policy , 2002, Math. Methods Oper. Res..

[138]  Peter J. Kolesar,et al.  Operating Characteristics of a Simple Shuttle under Local Dispatching Rules , 1972, Oper. Res..

[139]  N. K. Jaiswal,et al.  Optimal Operating Policies for the Finite-Source Queuing Process , 1972, Oper. Res..

[140]  Kuo-Hsiung Wang,et al.  Optimal control of an M/Hk/1 queueing system with a removable server , 2003, Math. Methods Oper. Res..

[141]  Vincent A. Mabert,et al.  AN EVALUATION OF ORDER RELEASE MECHANISMS IN A JOB-SHOP ENVIRONMENT , 1988 .

[142]  Alexei B. Piunovskiy.  Bicriteria Optimization of a Queue with a Controlled Input Stream , 2004, Queueing Syst. Theory Appl..

[143]  Jewgeni H. Dshalalow.  A note on D-policy bulk queueing systems , 2001, Journal of Applied Probability.

[144]  V. Balachandran,et al.  Comment on “Solving the 'Marketing Mix' Problem using Geometric Programming” , 1975 .

[145]  Hideaki Takagi,et al.  Queueing analysis: a foundation of performance evaluation , 1993 .

[146]  J. G. Shanthikumar.  Optimal Control of an M/G/1 Priority Queue Via N-Control , 1981 .

[147]  Israel Brosh,et al.  The Policy Space Structure of Markovian Systems with Two Types of Service , 1970 .

[148]  Henk C. Tijms,et al.  A Control Policy for a Priority Queue with Removable Server , 1974, Oper. Res..

[149]  R. Deb,et al.  Optimal control of batch service queues with switching costs , 1976 .

[150]  Awi Federgruen,et al.  Optimal Maintenance Policies for Single-Server Queueing Systems Subject to Breakdowns , 1990, Oper. Res..

[151]  Gang Chen,et al.  Optimal Management of a Removable and Non-Reliable Server in an Infinite and a Finite M/Hk/1 Queueing System , 2004 .

[152]  Ho Woo Lee,et al.  Queue Length Analysis of MAP/G/1 Queue Under D-Policy , 2004 .

[153]  Kuo-Hsiung Wang.  Optimal operation of a markovian queueing system with a removable and non-reliable server , 1995 .

[154]  Richard V. Evans.  Programming problems and changes in the stable behavior of a class of Markov chains , 1971 .

[155]  Kuo-Hsiung Wang,et al.  Optimal control of a removable server in an M/Ek/1 queueing system with finite capacity , 1995 .

[156]  Surendra M. Gupta,et al.  Duality relations for queues with arrival and service control , 1997, Comput. Oper. Res..

[157]  Gennadi Falin,et al.  A survey of retrial queues , 1990, Queueing Syst. Theory Appl..

[158]  Sun Hur,et al.  The effect of different arrival rates on the N-policy of M/G/1 with server setup , 1999 .