Stationary queuing systems with dependencies

The fundamental results relating to queuing systems with dependencies are presented in condensed form in the present survey. Particular attention is paid to the extension of the results obtained earlier for classical systems to systems with dependencies, and certain early classical results in queuing theory are discussed.

[1]  J. Kiefer,et al.  On the theory of queues with many servers , 1955 .

[2]  Manfred Schäl,et al.  The analysis of queues by state-dependent parameters by Markov renewal processes , 1971, Advances in Applied Probability.

[3]  R. Schassberger.  The insensitivity of stationary probabilities in networks of queues , 1978, Advances in Applied Probability.

[4]  A. Kuczura,et al.  Piecewise Markov Processes , 1973 .

[5]  Shaler Stidham,et al.  Semi-Stationary Clearing Processes. , 1978 .

[6]  L. Kleinrock.  A conservation law for a wide class of queueing disciplines , 1965 .

[7]  D. König,et al.  Stochastic inequalities between customer-stationary and time-stationary characteristics of queueing systems with point processes , 1980 .

[8]  D. König,et al.  Eine Invarianzeigenschaft zufälliger Bedienungsprozesse mit positiven Geschwindigkeiten , 1975 .

[9]  Masao Mori.  SOME BOUNDS FOR QUEUES , 1975 .

[10]  N. P. Leont'eva.  Convergence to limit processes in multichannel service systems , 1978 .

[11]  D. König,et al.  Invariante statlonäre zustandswahrscheinlichkeiten fur eine klasse stochastischer modelle mit f unktionellen abhangigkeiten , 1976 .

[12]  R. Wolff.  Work-conserving priorities , 1970 .

[13]  P. H. Brill,et al.  Level Crossings in Point Processes Applied to Queues: Single-Server Case , 1977, Oper. Res..

[14]  H. Rossberg,et al.  The GI/G/1 model with warming-up time , 1974 .

[15]  G. F. Newell,et al.  Introduction to the Theory of Queues. , 1963 .

[16]  Shaler Stidham,et al.  Technical Note - A Last Word on L = λW , 1974, Oper. Res..

[17]  Dietrich Stoyan,et al.  Qualitative Eigenschaften und Abschätzungen stochastischer Modelle , 1977 .

[18]  Norman Kaplan,et al.  Limit Theorems for a $GI/G/\infty$ Queue , 1975 .

[19]  K. T. Marshall,et al.  Customer average and time average queue lengths and waiting times , 1971 .

[20]  Ronald W. Wolff,et al.  AN EXTENSION OF ERLANG'S LOSS FORMULA , 1976 .

[21]  Ralph L. Disney,et al.  Random Flow in Queueing Networks: A Review and Critique , 1975 .

[22]  Gian-Carlo Rota,et al.  Stochastic processes in queuing theory: A. A. Borovkov, Springer, 1976, 280 pp. , 1977 .

[23]  C. Pearce.  On a many server queue with non-recurrent input and negative exponential servers , 1968, Journal of the Australian Mathematical Society.

[24]  Isi Mitrani,et al.  The Distribution of Queuing Network States at Input and Output Instants , 1979, JACM.

[25]  Ralph L. Disney,et al.  Some Problems of Queues with Feedback. , 1978 .

[26]  D. G. Tambouratzis,et al.  Erlang's formula and some results on the departure process for a loss system , 1973, Journal of Applied Probability.

[27]  Sreekantan S. Nair,et al.  A single server tandem queue , 1971, Journal of Applied Probability.

[28]  R. M. Loynes,et al.  On the Waiting‐Time Distribution for Queues in Series , 1965 .

[29]  D. König.  Stochastic processes with basic stationary marked point processes , 1977, Advances in Applied Probability.

[30]  D. Stoyan,et al.  A quantitative continuity theorem for the mean stationary waiting time in GI/GI/1 , 1976 .

[31]  Peter Purdue,et al.  The M/M/1 Queue in a Markovian Environment , 1974, Oper. Res..

[32]  W. Whitt.  The continuity of queues , 1974, Advances in Applied Probability.

[33]  Donald L. Snyder,et al.  Random point processes , 1975 .

[34]  Boris Gnedenko,et al.  Einführung in die Bedienungstheorie , 1971 .

[35]  D. Iglehart.  Multiple channel queues in heavy traffic , 1971, Advances in Applied Probability.

[36]  Shaler Stidham,et al.  L = λW: A Discounted Analogue and a New Proof , 1972, Oper. Res..

[37]  Ward Whitt,et al.  Continuity of Generalized Semi-Markov Processes , 1980, Math. Oper. Res..

[38]  M. Neuts.  Two queues in series with a finite, intermediate waitingroom , 1968, Journal of Applied Probability.

[39]  D. Kendall.  Some Problems in the Theory of Queues , 1951 .

[40]  D. Kendall.  Stochastic Processes Occurring in the Theory of Queues and their Analysis by the Method of the Imbedded Markov Chain , 1953 .

[41]  T. Lewis,et al.  The Intervals between Regular Events Displaced in Time by Independent Random Deviations of Large Dispersion , 1961 .

[42]  Robert Harris.  Technical Note - The Expected Number of Idle Servers in a Queuing System , 1974, Oper. Res..

[43]  TRAFFIC LIGHT QUEUES WITH DEPENDENT ARRIVALS AS A GENERALIZATION TO QUEUEING THEORY , 1972 .

[44]  Convergence theorems for queueing and waiting-time processes with continuous time , 1976 .

[45]  P. Brémaud.  Point processes and queues, martingale dynamics , 1983 .

[46]  Rosser T. Nelson,et al.  Queueing network experiments with varying arrival and service processes , 1966 .

[47]  Vincent Hodgson,et al.  The Single Server Queue. , 1972 .

[48]  D. P. Kennedy.  THE CONTINUITY OF THE SINGLE SERVER QUEUE , 1972 .

[49]  W. Feller.  Fluctuation theory of recurrent events , 1949 .

[50]  Dieter König.  Verallgemeinerungen der Engsetschen Formel , 1964 .

[51]  P. D. Finch.  On the distribution of queue size in queueing problems , 1959 .

[52]  Erhan Cinlar,et al.  Markov Renewal Theory: A Survey , 1973 .

[53]  Woollcott Smith.  Technical Note - The Infinitely-Many-Server Queue with Semi-Markovian Arrivals and Customer-Dependent Exponential Service Times , 1972, Oper. Res..

[54]  V. Rykov.  Regenerative processes with embedded regeneration periods and their application to the investigation of priority queuing systems , 1975 .

[55]  C. Pearce.  Queues with moving average service times , 1967, Journal of Applied Probability.

[56]  G. Shedler,et al.  Simulation of nonhomogeneous Poisson processes with log linear rate function , 1976 .

[57]  J. Mecke.  Das erlangsche model mit abhängigen bedienungszeiten , 1972 .

[58]  B. Lemaire.  Méthode de conservation et blocage dans les files d'attente , 1977 .

[59]  Henry D. Friedman,et al.  Reduction Methods for Tandem Queuing Systems , 1965 .

[60]  B. A. Sevast'yanov.  An Ergodic Theorem for Markov Processes and Its Application to Telephone Systems with Refusals , 1957 .

[61]  R. Schassberger.  Insensitivity of steady-state distributions of generalized semi-Markov processes by speeds , 1978, Advances in Applied Probability.

[62]  I. Sahin,et al.  Equilibrium behavior of a stochastic system with secondary input , 1971 .

[63]  W. Whitt.  Embedded renewal processes in the GI/G/s queue , 1972, Journal of Applied Probability.

[64]  Charles D. Pack.  A Comparison of the Output Process of an $M/D/ 1$ Queue as Measured from an Arbitrary Departure Epoch to That Measured from an Arbitrary Instant in Time , 1975 .

[65]  B. Grigelionis.  Random point processes and martingales , 1975 .

[66]  N. K. Jaiswal,et al.  Priority queues , 1968 .

[67]  G. F. Newell,et al.  A relation between stationary queue and waiting time distributions , 1971, Journal of Applied Probability.

[68]  Austin J. Lemoine.  State-of-the-Art---Networks of Queues---A Survey of Equilibrium Analysis , 1977 .

[69]  Gerold Pestalozzi,et al.  A queue with Markov-dependent service times , 1968, Journal of Applied Probability.

[70]  P. Brémaud.  Streams of a M/M/1 feedback queue in statistical equilibrium , 1978 .

[71]  V. Schmidt.  On some relations between stationary time and customer state probabilities for qneueing systems G/GI/s/r , 1978 .

[72]  B. W. Conolly,et al.  The Waiting Time Process for a Certain Correlated Queue , 1968, Oper. Res..

[73]  Shelby Brumelle,et al.  A Generalization of L = λW to Moments of Queue Length and Waiting Times , 1972, Oper. Res..

[74]  K. Nawrotzki.  Einige bemerkungen zur verwendung der palmschen verteilung in der bedienungstheorie , 1978 .

[75]  F. Kelly,et al.  Networks of queues , 1976, Advances in Applied Probability.

[76]  J. Sacks.  Ergodocity of Queues in Series , 1960 .

[77]  E. Reich.  Note on Queues in Tandem , 1963 .

[78]  Edward Ignall,et al.  An extension of Erlang's formulas which distinguishes individual servers , 1972, Journal of Applied Probability.

[79]  Onno Boxma.  The single-server queue with random service output , 1975 .

[80]  J. Jacod,et al.  Processus ponctuels et martingales: résultats récents sur la modélisation et le filtrage , 1977 .

[81]  Richard Loulou.  MULTI-CHANNEL QUEUES IN HEAVY TRAFFIC , 1973 .

[82]  Linus Schrage.  Letter to the Editor - An Alternative Proof of a Conservation Law for the Queue G/G/1 , 1970, Oper. Res..

[83]  D. Lampard.  A stochastic process whose successive intervals between events form a first order Markov chain — I , 1968, Journal of Applied Probability.

[84]  P. D. Finch.  The single server queueing system with Non-recurrent input-process and Erlang service time , 1963 .

[85]  D. Iglehart,et al.  Multiple channel queues in heavy traffic. I , 1970, Advances in Applied Probability.

[86]  Hisashi Kobayashi,et al.  Accuracy of the diffusion approximation for some queuing systems , 1974 .

[87]  W. Winkler.  D. König u. a. Verallgemeinerungen der Erlangschen und Engsetschen Formeln. (Schriftenreihe d. Inst. f. Math. b. d. DAdW Heft 5). 123 S. m. 1 Abb. Berlin 1967. Akademie-Verlag. Preis brosch. 28,70 M , 1969 .

[88]  A. Barbour.  Networks of queues and the method of stages , 1976, Advances in Applied Probability.

[89]  Weak convergence in an appointment system , 1975 .

[90]  Volker Schmidt,et al.  On Time-dependent and Stationary Queue Length Characteristics , 1980, J. Inf. Process. Cybern..

[91]  J. Mecke,et al.  Stationäre ERLANGsche Prozesse , 1975 .

[92]  David Vere-Jones,et al.  Some Applications of Probability Generating Functionals to the Study of Input-Output Streams , 1968 .

[93]  S. Schönherr.  Limit theorems for single server queues with mixed renewal and poisson inputs , 1979 .

[94]  W. J. Gordon,et al.  Closed Queuing Systems with Exponential Servers , 1967, Oper. Res..

[95]  J. Kingman.  Some inequalities for the queue GI/G/1 , 1962 .

[96]  C. R. Heathcote,et al.  An Approximation for the Moments of Waiting Times , 1969, Oper. Res..

[97]  M. Miyazawa.  A formal approach to queueing processes in the steady state and their applications , 1979 .

[98]  Marcel F. Neuts,et al.  Exponential Ergodicity of the $M/G/1$ Queue , 1969 .

[99]  S. O. Rice.  Single server systems — I. Relations between some averages , 1962 .

[100]  M. Posner,et al.  Single-Server Queues with Service Time Dependent on Waiting Time , 1973, Oper. Res..

[101]  S. Stidham.  Regenerative processes in the theory of queues, with applications to the alternating-priority queue , 1972, Advances in Applied Probability.

[102]  Elja Arjas,et al.  On the use of a fundamental identity in the theory of semi-Markov queues , 1972, Advances in Applied Probability.

[103]  Austin J. Lemoine,et al.  Limit Theorems for Periodic Queues , 1977 .

[104]  Carl M. Harris,et al.  A Note on Feedback Queues with Bulk Service , 1972, JACM.

[105]  Uwe Jansen.  Unempfindlichkeitseigenschaft für verschiedene Auswahlregeln ohne Vorliegen der Produktform der stationären Verteilung , 1980, J. Inf. Process. Cybern..

[106]  Uwe Jansen,et al.  Ergebnisse von invarianzuntersuchnngen fr ausgewhlte bedienungs- und zuverlssigkeitssysteme , 1976 .

[107]  Donald F. Towsley,et al.  Product Form and Local Balance in Queueing Networks , 1977, JACM.

[108]  B. Kopocinski,et al.  Steady-state distributions of queue length in the GI/G/s queue , 1977 .

[109]  D. C. McNickle.  The number of departures from a semi-Markov queue , 1974 .

[110]  Klaus Matthes,et al.  Verallgemeinerungen der Erlangschen Formeln. I , 1963 .

[111]  On the output theorem of queueing theory, via filtering , 1978 .

[112]  L. Takács.  THE LIMITING DISTRIBUTION OF THE VIRTUAL WAITING TIME AND THE QUEUE SIZE FOR A SINGLE-SERVER QUEUE WITH RECURRENT INPUT AND GENERAL SERVICE TIMES , 1963 .

[113]  V. A. Kokotuskin.  A Generalization of the Palm–Khinchin Theorem , 1975 .

[114]  Austin J. Lemoine,et al.  Technical Note - Approximations for a Service System with Nonindependent Interarrival Times , 1975, Oper. Res..

[115]  D. Iglehart,et al.  Multiple channel queues in heavy traffic. II: sequences, networks, and batches , 1970, Advances in Applied Probability.

[116]  D. N. Shanbhag.  Some extensions of Takács's limit theorems , 1974 .

[117]  Austin J. Lemoine,et al.  Limit theorems for generalized single server queues , 1974, Advances in Applied Probability.

[118]  D. Cox.  The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables , 1955, Mathematical Proceedings of the Cambridge Philosophical Society.

[119]  Brève communication. Théorème de conservation des clients dans les files d'attente , 1978 .

[120]  E. Çinlar.  Exceptional Paper---Markov Renewal Theory: A Survey , 1975 .

[121]  L. Takács.  A single-server queue with limited virtual waiting time , 1974, Journal of Applied Probability.

[122]  P. J. Burke.  Technical Note - Delays in Single-Server Queues with Batch Input , 1975, Oper. Res..

[123]  Rainer Gutjahr,et al.  Eine bemerkung zur existenz unendllcli vieler ”leorpunkte“ in bedienungssystemen liiit liiienillm-li vleleii bedienungsgeräten , 1977 .

[124]  B. Lisek.  Construction of stationary state distributions for loss systems , 1979 .

[125]  M. Krakowski.  Arrival and departure processes in queues. Pollaczek-Khintchine formulas for bulk arrivals and bounded systems , 1974 .

[126]  Н. В. Яровицкий.  О некоторых свойствах односвязно-зависимых потоков@@@On some properties of simple connected dependent flows , 1962 .

[127]  Richard J Swersey.  CLOSED NETWORKS OF QUEUES , 1967 .

[128]  V. Zolotarev.  On the Continuity of Stochastic Sequences Generated by Recurrent Processes , 1976 .

[129]  A note on the queueing system GI / G /∞ , 1968 .

[130]  R. M. Loynes.  The stability of a system of queues in series , 1964 .

[131]  Lajos Takács,et al.  A queuing model with feedback , 1977 .

[132]  D. V. Lindley,et al.  The theory of queues with a single server , 1952, Mathematical Proceedings of the Cambridge Philosophical Society.

[133]  A. Karr.  Weak convergence of a sequence of Markov chains , 1975 .

[134]  Aleksandr Alekseevich Borovkov,et al.  Asymptotic methods in queuing theory , 1984 .

[135]  B. Melamed.  Characterizations of Poisson traffic streams in Jackson queueing networks , 1979, Advances in Applied Probability.

[136]  Carl M. Harris,et al.  Some Results for Bulk-Arrival Queues with State-Dependent Service Times , 1970 .

[137]  D. Kendall.  Some Recent Work and Further Problems in the Theory of Queues , 1964 .

[138]  Woollcott Smith,et al.  Shot noise generated by a semi-Markov process , 1973, Journal of Applied Probability.

[139]  J. Teugels,et al.  The exponential rate of convergence of the distribution of the maximum of a random walk. Part II , 1975 .

[140]  V. Zolotarev.  METRIC DISTANCES IN SPACES OF RANDOM VARIABLES AND THEIR DISTRIBUTIONS , 1976 .

[141]  Marcel F. Neuts,et al.  The Infinite-Server Queue with Poisson Arrivals and Semi-Markovian Services , 1972, Oper. Res..

[142]  Austin J. Lemoine,et al.  On the virtual and actual waiting time distributions of a GI/G/ 1 queue , 1976 .

[143]  M. Neuts.  A QUEUE SUBJECT TO EXTRANEOUS PHASE CHANGES , 1971 .

[144]  Masakiyo Miyazawa.  Time and customer processes in queues with stationary inputs , 1977 .

[145]  M. Schal,et al.  Markov Renewal Processes with Auxiliary Paths , 1970 .

[146]  E. CastroPeter,et al.  Infinitely Divisible Point Processes , 1982 .

[147]  J. R. Callahan.  A queue with waiting time dependent service times , 1973 .

[148]  T. Roslki.  A note on queues with a common traffic intensity , 1979 .

[149]  Teresa Ryba.  Remark on a Service System with Mixed Input Streams , 1972, Oper. Res..

[150]  H. C. Tijms,et al.  A simple proof of the equivalence of the limiting distributions of the continuous-time and the embedded process of the queue size in the m/g/1 queue , 1976 .

[151]  D. Stoyan,et al.  On some belations between stationary distributions of queue lengths and imbedded queue lengths in g/g/s queueing systems , 1976 .

[152]  M. L. Chaudhry,et al.  Marriage between the Supplementary Variable Technique and the Imbedded Markov Chain Technique-I , 1978 .

[153]  Y. K. Belyaev.  Limit Theorems for Dissipative Flows , 1963 .

[154]  P. Brémaud.  Point Processes and Queues , 1981 .

[155]  Note on Palm measures in the intensity conservation law and inversion formula in PMP and their applications , 1981 .

[156]  Marcel F Neuts,et al.  Further Results on the M/M/1 Queue with Randomly Varying Rates. , 1978 .

[157]  Marcel F. Neuts.  The single server queue with Poisson input and semi-Markov service times , 1966 .

[158]  Peter Franken.  Erlangsche Formeln für semimarkowschen Eingang , 1968, J. Inf. Process. Cybern..

[159]  M. Neuts.  Some explicit formulas for the steady-state behavior of the queue with semi-Markovian service times , 1977, Advances in Applied Probability.

[160]  Richard F. Serfozo,et al.  Semi-stationary processes , 1972 .

[161]  Peter Purdue.  A queue with poisson input and semi-Markov service times: busy period analysis , 1975 .

[162]  E. Çinlar.  Markov renewal theory , 1969, Advances in Applied Probability.

[163]  Tomasz Rolski,et al.  Piecewise Markov processes on a general state space , 1977 .

[164]  A result on the output of stationary Erlang processes , 1975 .

[165]  D. Stoyan,et al.  Stabilitätssätze für eine Klasse homogener MARKOWscher Prozesse , 1974 .

[166]  Guy Pujolle,et al.  Recurrence in single server queues with impatient customers , 1978 .

[167]  D. Stoyan.  Further stochastic order relations among GI/GI/1 queues with a common traffic intensity , 1977 .

[168]  Percy H. Brill,et al.  An embedded level crossing technique for dams and queues , 1979, Journal of Applied Probability.

[169]  M. Kotzubes.  Further bounds for waiting time distributions and their means in the case ρ<1 , 1979 .

[170]  R. Pyke,et al.  The Existence and Uniqueness of Stationary Measures for Markov Renewal Processes , 1966 .

[172]  Tomasz Rolski,et al.  A rate-conservative principle for stationary piecewise Markov processes , 1978, Advances in Applied Probability.

[173]  Ursula Kalähnea.  Existence, uniqueness and some in variance properties of stationary distributions for general single server queues , 1976 .

[174]  B. W. Conolly,et al.  Generalised birth and death queueing processes: recent results , 1977, Advances in Applied Probability.

[175]  L. Delbrouck.  A set of Wiener-Hopf integral equations with common solution in fluctuation theory , 1973 .

[176]  A. Kuczura.  Loss Systems with Mixed Renewal and Poisson Inputs , 1973, Oper. Res..

[177]  S. Brumelle.  On the relation between customer and time averages in queues , 1971 .

[178]  E. Çinlar.  Time dependence of queues with semi-Markovian services , 1967, Journal of Applied Probability.

[179]  Comments of the paper, “stochastic integral equations applied to telecommunications traffic without delay” , 1978 .

[180]  Uwe Jansen,et al.  Stochastic Processes and Properties of Invariance for Queueing Systems with Speeds and Temporary Interruptions , 1977 .

[181]  J D Littler,et al.  A PROOF OF THE QUEUING FORMULA , 1961 .

[182]  Boundary properties of distributions for states of systems with variable structure of demand service under control of conflict flows in a class of nonlinear homogeneous algorithms. III , 1977 .

[183]  Uwe Jansen,et al.  Insensitivity and Steady-state Probabilities in Product Form for Queueing Networks , 1980, J. Inf. Process. Cybern..

[184]  Takehisa Fujisawa,et al.  EFFECTS OF MULTIPLICITY IN ARRIVAL PROCESSES ON QUEUE LENGTHS AND WAITING TIMES , 1976 .

[185]  D. Stoyan,et al.  A Remark on the Stability of the Stationary Distributions of MARKOV Chains , 1977 .

[186]  Douglas R. Miller,et al.  Translated Renewal Processes and the Existence of a Limiting Distribution for the Queue Length of the GI/G/s Queue , 1975 .

[187]  I. I. Ezhov,et al.  Ergodic Theorems Connected with the Markov Property of Random Processes , 1977 .

[188]  Walter L. Smith.  Renewal Theory and its Ramifications , 1958 .

[189]  S. Ross.  Average delay in queues with non-stationary Poisson arrivals , 1978, Journal of Applied Probability.

[190]  P. Franken,et al.  Existence, Uniqueness and Continuity of Stationary Distributions for Queueing Systems without Delay , 1978 .

[191]  W. Whitt.  Multiple channel queues in heavy traffic. III: random server selection , 1970, Advances in Applied Probability.

[192]  Masao Mori,et al.  Relations between queue-size and waiting-time distributions , 1980, Journal of Applied Probability.

[193]  Austin J. Lemoine.  On two stationary distributions for the stable GI/G/1 queue , 1974 .

[194]  D. P. Kennedy.  A note on the number of busy servers in a GI/G/s queue in light traffic , 1972 .

[195]  Ralph L. Disney,et al.  Queues with Instantaneous Feedback , 1977 .

[196]  D. Daley,et al.  Queueing output processes , 1976, Advances in Applied Probability.

[197]  M. Neuts.  Markov chains with applications in queueing theory, which have a matrix-geometric invariant probability vector , 1978, Advances in Applied Probability.

[198]  L. Takács.  On Erlang's Formula , 1969 .

[199]  Linus Schrage,et al.  The Queue M/G/1 with the Shortest Remaining Processing Time Discipline , 1966, Oper. Res..

[200]  Approximations for a Service System with Non-Independent Interarrival Times. , 1973 .

[201]  P. D. Finch.  A probability limit theorem with application to a generalisation of queueing theory , 1959 .

[202]  Frank Kelly,et al.  Reversibility and Stochastic Networks , 1979 .

[203]  David Oakes,et al.  Random Overlapping Intervals--A Generalization of Erlang's Loss Formula , 1976 .

[204]  Stationäre Verteilungen für das Erlangsche Modell , 1973 .

[205]  V. Schmidt,et al.  Queues and Point Processes , 1983 .

[206]  Dietrich Stoyan,et al.  Stochastic processes with imbedded marked point processes (pmp) and thcir application in queneing , 1978 .

[207]  R. M. Loynes,et al.  The stability of a queue with non-independent inter-arrival and service times , 1962, Mathematical Proceedings of the Cambridge Philosophical Society.

[208]  Austin J. Lemoine,et al.  Limit Theorems for Generalized Single Server Queues: The Exceptional System , 1975 .

[209]  F. Chariot,et al.  Irréductibilité et récurrence au sens de Harris des «Temps d'attente→ des files GI/G/q , 1978 .

[210]  J. Harrison.  Assembly-like queues , 1973, Journal of Applied Probability.

[211]  Thomas M. O'Donovan.  Technical Note - Distribution of Attained and Residual Service in General Queuing Systems , 1974, Oper. Res..

[212]  H. Rossberg.  Über die Verteilung von Wartezeiten , 1965 .

[213]  K. Mani Chandy,et al.  Open, Closed, and Mixed Networks of Queues with Different Classes of Customers , 1975, JACM.

[214]  Marcel F Neuts,et al.  The M/M/1 Queue with Randomly Varying Arrival and Service Rates. , 1977 .

[215]  R. Schassberger.  Insensitivity of Steady-state Distributions of Generalized Semi-Markov Processes. Part II , 1977 .

[216]  M. Neuts,et al.  The infinite server queue with semi-Markovian arrivals and negative exponential services , 1972, Journal of Applied Probability.

[218]  A. Barbour,et al.  INSENSITIVE AVERAGE RESIDENCE TIMES IN GENERALIZED SEMI-MARKOV PROCESSES , 1981 .

[219]  J. W. Cohen.  ON A SINGLE-SERVER QUEUE WITH GROUP ARRIVALS , 1976 .

[220]  A. Kuczura,et al.  Queues with mixed renewal and poisson inputs , 1972 .

[221]  D. Iglehart.  Weak convergence in queueing theory , 1973, Advances in Applied Probability.

[222]  Peter A. W. Lewis,et al.  Stochastic point processes : statistical analysis, theory, and applications , 1973 .

[223]  Bernard P. Zeigler,et al.  Equilibrium Properties of Arbitrarily Interconnected Queueing Networks. , 1975 .

[224]  Dieter König.  Methods for Proving Relationships between Stationary Characteristics of Queueing Systems with Point Processes , 1980, J. Inf. Process. Cybern..

[225]  Jacob Cohen,et al.  On up- and downcrossings , 1977, Journal of Applied Probability.

[226]  Walter L. Smith,et al.  Regenerative stochastic processes , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[227]  D. König,et al.  Imbedded and non-imbedded stationary characteristics of queueing systems with varying service rate and point processes , 1980 .

[228]  K. T. Marshall.  Bounds for Some Generalizations of the GI/G/1 Queue , 1968, Oper. Res..

[229]  Masakiyo Miyazawa,et al.  STOCHASTIC ORDER RELATIONS AMONG GI/G/1 QUEUES WITH A COMMON TRAFFIC INTENSITY , 1976 .

[230]  Johannes Kerstan,et al.  Unbegrenzt teilbare Punktprozesse , 1974 .

[231]  Ralph E. Strauch,et al.  When a Queue Looks the Same to an Arriving Customer as to an Observer , 1970 .

[232]  K. Murari.  A Queueing Problem with Correlated Arrivals and General Service Time Distribution , 1969 .

[233]  C. R. Heathcote,et al.  Complete exponential convergence and some related topics , 1967, Journal of Applied Probability.

[234]  C. Heathcote,et al.  On the rate of convergence of waiting times , 1965, Journal of the Australian Mathematical Society.

[235]  M. Krakowski.  Conservation methods in queuing theory , 1973 .

[237]  Dénes König,et al.  Verallgemeinerungen der Erlangschen und Engsetschen Formeln : Eine Methode in der Bedienungstheorie , 1967 .

[238]  Roger B. Nelsen,et al.  Random displacements of regularly spaced events , 1970 .

[239]  P. D. Finch,et al.  A second look at a queueing system with moving average input process , 1965 .

[240]  U. Jansen,et al.  A criterion of insensitivity for a class of queueing systems with random marked point processes , 1979 .

[241]  J. Little.  A Proof for the Queuing Formula: L = λW , 1961 .

[242]  Peter Franken,et al.  Einige Anwendungen der Theorie zufälliger Punktprozesse in der Bedienungstheorie I , 1975 .

[243]  Shelby Brumelle.  A Generalization of Erlang's Loss System to State Dependent Arrival and Service Rates , 1978, Math. Oper. Res..

[244]  E. Çinlar.  QUEUES WITH SEMI-MARKOVIAN ARRIVALS , 1967 .