5.5. Remarks and references

Chapters in this book

1. Frontmatter 1
2. Preface 5
3. Contents 9
4. 1. Random marked point processes and processes with an embedded marked point process
5. 1.0. Introduction 13
6. 1.1. Random marked point processes 14
7. 1.2. Stationary RMPP's. The Palm distribution 21
8. 1.3. Characterizations of the Palm distribution 29
9. 1.4. The distribution P⁰_L 39
10. 1.5. Processes with embedded marked point process 44
11. 1.6. Intensity conservation principle 47
12. 1.7. Remarks and references 53
13. 2. Time- and customer-stationary processes for queueing systems. Existence and ergodic theorems
14. 2.0. Introduction 58
15. 2.1. Notations 60
16. 2.2. General approach to existence, uniqueness and ergodic theorems First we shall make 62
17. 2.3. Systems without delay 68
18. 2.4. Systems with delay 77
19. 2.5. Remarks and references 86
20. 3. Continuity theorems for time- and customer-stationary quantities
21. 3.0. Introduction 88
22. 3.1. Systems without delay 89
23. 3.2. Systems with delay 95
24. 3.3. Remarks and references 101
25. 4. Relationships between time- and customer-stationary quantities. I: Basic systems
26. 4.0. Introduction 104
27. 4.1. Systems with a Poisson process of arrival instants 105
28. 4.2. Little's formulae 106
29. 4.3. The number of customers 111
30. 4.4. Some formulae concerning busy cycles 124
31. 4.5. Extensions of Takács' formulae for G/G/1/∞ 126
32. 4.6. The work load in G/G/s/r 130
33. 4.7. Repairman problem 138
34. 4.8. Remarks and references 139
35. 5. Relationships between time- and customer-stationary quantities. II: Further systems
36. 5.0. Introduction 143
37. 5.1. Several customer types 143
38. 5.2. Group arrivals 150
39. 5.3. Varying service rate 152
40. 5.4. Uniformly bounded work load; warming up 155
41. 5.5. Remarks and references 157
42. 6. Insensitivity of stationary state probabilities for a class of queueing systems
43. 6.0. Introduction 160
44. 6.1. General queueing systems 161
45. 6.2. Construction of a suitable queueing process 163
46. 6.3. The equation system Z and the property E((I_j)_j€J) 166
47. 6.4. The main result 167
48. 6.5. Embedded probabilities and mean sojourn times of insensitive systems 171
49. 6.6. Poisson output of an insensitive queueing system 172
50. 6.7. Examples 174
51. 6.8. The structure of insensitive queueing systems 183
52. 6.9. Remarks and references 186
53. Bibliography 190
54. Result Index 200
55. Symbol Index 202
56. Index 206