Polling systems.

*(English)*Zbl 0932.90007
CWI Tracts. 115. Amsterdam: CWI. vi, 232 p. (1996).

This monograph is a useful addition to the large literature on polling systems. After a synopsis of standard models and existing analysis techniques, the author obtains several generalizations of known results through the study of single server queues with service interruptions; the main tool, for which an alternative, short derivation is given is the M/G/1 queue length decomposition law of S. W. Fuhrmann and R. B. Cooper [Oper. Res. 33, 1117-1129 (1985; Zbl 0585.90033)].

Attention is then turned to polling systems in which a so-named dormant server is allowed to halt at a queue when the whole system is empty: this begs the question of where the server should halt to maximize performance. The optimization theme continues with investigations into \(k\)-limited service strategies and fixed time polling schemes (where both the order and starting times of queue visits are prescribed); waiting time approximations are used to form tractable objective functions. The monograph concludes by addressing multiple server systems, which have received much less coverage to date. First there is analytical discussion of a nonlinear programming formulation of a load-sharing problem with heterogeneous customers and servers. Then two generalized polling systems are considered: one with a single multi-server and the other with several independent individual servers.

The chapters comprise: 1. Introduction, 2. Decomposition properties and pseudo-conservation laws in polling models, 3. Polling systems with zero and non-zero switch-over times, 4. A pseudo-conservation law for a polling system with a dormant server, 5. A globally gated polling system with a dormant server, 6. Optimization of \(k\)-limited service strategies, 7. Optimization of fixed time polling schemes, 8. Optimization allocation of customer types to servers, 9. Polling systems with multiple coupled servers, 10. Waiting-time approximations for multiple-server polling systems.

There is an extensive bibliography.

Attention is then turned to polling systems in which a so-named dormant server is allowed to halt at a queue when the whole system is empty: this begs the question of where the server should halt to maximize performance. The optimization theme continues with investigations into \(k\)-limited service strategies and fixed time polling schemes (where both the order and starting times of queue visits are prescribed); waiting time approximations are used to form tractable objective functions. The monograph concludes by addressing multiple server systems, which have received much less coverage to date. First there is analytical discussion of a nonlinear programming formulation of a load-sharing problem with heterogeneous customers and servers. Then two generalized polling systems are considered: one with a single multi-server and the other with several independent individual servers.

The chapters comprise: 1. Introduction, 2. Decomposition properties and pseudo-conservation laws in polling models, 3. Polling systems with zero and non-zero switch-over times, 4. A pseudo-conservation law for a polling system with a dormant server, 5. A globally gated polling system with a dormant server, 6. Optimization of \(k\)-limited service strategies, 7. Optimization of fixed time polling schemes, 8. Optimization allocation of customer types to servers, 9. Polling systems with multiple coupled servers, 10. Waiting-time approximations for multiple-server polling systems.

There is an extensive bibliography.

Reviewer: J.Preater (Keele)

##### MSC:

90B22 | Queues and service in operations research |

90-02 | Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming |

60K25 | Queueing theory (aspects of probability theory) |