annihilation

Chen, Anyue and Renshaw, Eric (2000) Existence, recurrence and equilibrium properties of Markov branching processes with instantaneous immigration. Stochastic Processes and their Applications, 88 (2). pp. 177-193. ISSN 0304-4149 (doi:10.1016/S0304-4149(99)00125-8)

Renshaw, Eric and Chen, Anyue (1997) Birth-death processes with mass annihilation and state-dependent immigration. Communications in Statistics. Stochastic Models, 13 (2). pp. 239-253. ISSN 0882-0287 (doi:10.1080/15326349708807424)

birth-death process

Renshaw, Eric and Chen, Anyue (1997) Birth-death processes with mass annihilation and state-dependent immigration. Communications in Statistics. Stochastic Models, 13 (2). pp. 239-253. ISSN 0882-0287 (doi:10.1080/15326349708807424)

bulk arrival

Chen, Anyue and Renshaw, Eric (2004) Markovian bulk-arriving queues with state-dependent control at idle time. Advances in Applied Probability, 36 (2). pp. 499-524. ISSN 1475-6064 (Print), 0001-8678 (Online) (doi:10.1239/aap/1086957583)

busy period distribution

Chen, Anyue and Renshaw, Eric (2004) Markovian bulk-arriving queues with state-dependent control at idle time. Advances in Applied Probability, 36 (2). pp. 499-524. ISSN 1475-6064 (Print), 0001-8678 (Online) (doi:10.1239/aap/1086957583)

catastrophe

Chen, Anyue and Renshaw, Eric (2000) Existence, recurrence and equilibrium properties of Markov branching processes with instantaneous immigration. Stochastic Processes and their Applications, 88 (2). pp. 177-193. ISSN 0304-4149 (doi:10.1016/S0304-4149(99)00125-8)

Renshaw, Eric and Chen, Anyue (1997) Birth-death processes with mass annihilation and state-dependent immigration. Communications in Statistics. Stochastic Models, 13 (2). pp. 239-253. ISSN 0882-0287 (doi:10.1080/15326349708807424)

equilibrium distribution

Chen, Anyue and Renshaw, Eric (2004) Markovian bulk-arriving queues with state-dependent control at idle time. Advances in Applied Probability, 36 (2). pp. 499-524. ISSN 1475-6064 (Print), 0001-8678 (Online) (doi:10.1239/aap/1086957583)

Chen, Anyue and Renshaw, Eric (2000) Existence, recurrence and equilibrium properties of Markov branching processes with instantaneous immigration. Stochastic Processes and their Applications, 88 (2). pp. 177-193. ISSN 0304-4149 (doi:10.1016/S0304-4149(99)00125-8)

Renshaw, Eric and Chen, Anyue (1997) Birth-death processes with mass annihilation and state-dependent immigration. Communications in Statistics. Stochastic Models, 13 (2). pp. 239-253. ISSN 0882-0287 (doi:10.1080/15326349708807424)

existence

Chen, Anyue and Renshaw, Eric (2000) Existence, recurrence and equilibrium properties of Markov branching processes with instantaneous immigration. Stochastic Processes and their Applications, 88 (2). pp. 177-193. ISSN 0304-4149 (doi:10.1016/S0304-4149(99)00125-8)

factorial moments

Renshaw, Eric and Chen, Anyue (1997) Birth-death processes with mass annihilation and state-dependent immigration. Communications in Statistics. Stochastic Models, 13 (2). pp. 239-253. ISSN 0882-0287 (doi:10.1080/15326349708807424)

idle time

Chen, Anyue and Renshaw, Eric (2004) Markovian bulk-arriving queues with state-dependent control at idle time. Advances in Applied Probability, 36 (2). pp. 499-524. ISSN 1475-6064 (Print), 0001-8678 (Online) (doi:10.1239/aap/1086957583)

Markov branching process

Chen, Anyue and Renshaw, Eric (2000) Existence, recurrence and equilibrium properties of Markov branching processes with instantaneous immigration. Stochastic Processes and their Applications, 88 (2). pp. 177-193. ISSN 0304-4149 (doi:10.1016/S0304-4149(99)00125-8)

mass immigration

Renshaw, Eric and Chen, Anyue (1997) Birth-death processes with mass annihilation and state-dependent immigration. Communications in Statistics. Stochastic Models, 13 (2). pp. 239-253. ISSN 0882-0287 (doi:10.1080/15326349708807424)

mathematics

Chen, Anyue and Renshaw, Eric (1997) The M/M/1 queue with mass exodus and mass arrivals when empty. Journal of Applied Probability, 34 (1). pp. 192-207. ISSN 0021-9002

occupation probabilities

Renshaw, Eric and Chen, Anyue (1997) Birth-death processes with mass annihilation and state-dependent immigration. Communications in Statistics. Stochastic Models, 13 (2). pp. 239-253. ISSN 0882-0287 (doi:10.1080/15326349708807424)

q-matrix

Chen, Anyue and Renshaw, Eric (2000) Existence, recurrence and equilibrium properties of Markov branching processes with instantaneous immigration. Stochastic Processes and their Applications, 88 (2). pp. 177-193. ISSN 0304-4149 (doi:10.1016/S0304-4149(99)00125-8)

queue size

Chen, Anyue and Renshaw, Eric (2004) Markovian bulk-arriving queues with state-dependent control at idle time. Advances in Applied Probability, 36 (2). pp. 499-524. ISSN 1475-6064 (Print), 0001-8678 (Online) (doi:10.1239/aap/1086957583)

recurrence

Chen, Anyue and Renshaw, Eric (2004) Markovian bulk-arriving queues with state-dependent control at idle time. Advances in Applied Probability, 36 (2). pp. 499-524. ISSN 1475-6064 (Print), 0001-8678 (Online) (doi:10.1239/aap/1086957583)

Chen, Anyue and Renshaw, Eric (2000) Existence, recurrence and equilibrium properties of Markov branching processes with instantaneous immigration. Stochastic Processes and their Applications, 88 (2). pp. 177-193. ISSN 0304-4149 (doi:10.1016/S0304-4149(99)00125-8)

resolvent

Chen, Anyue and Renshaw, Eric (2000) Existence, recurrence and equilibrium properties of Markov branching processes with instantaneous immigration. Stochastic Processes and their Applications, 88 (2). pp. 177-193. ISSN 0304-4149 (doi:10.1016/S0304-4149(99)00125-8)

Renshaw, Eric and Chen, Anyue (1997) Birth-death processes with mass annihilation and state-dependent immigration. Communications in Statistics. Stochastic Models, 13 (2). pp. 239-253. ISSN 0882-0287 (doi:10.1080/15326349708807424)

state-dependent immigration

Chen, Anyue and Renshaw, Eric (2000) Existence, recurrence and equilibrium properties of Markov branching processes with instantaneous immigration. Stochastic Processes and their Applications, 88 (2). pp. 177-193. ISSN 0304-4149 (doi:10.1016/S0304-4149(99)00125-8)

state-dependent input

Chen, Anyue and Renshaw, Eric (2004) Markovian bulk-arriving queues with state-dependent control at idle time. Advances in Applied Probability, 36 (2). pp. 499-524. ISSN 1475-6064 (Print), 0001-8678 (Online) (doi:10.1239/aap/1086957583)

uniqueness

Renshaw, Eric and Chen, Anyue (1997) Birth-death processes with mass annihilation and state-dependent immigration. Communications in Statistics. Stochastic Models, 13 (2). pp. 239-253. ISSN 0882-0287 (doi:10.1080/15326349708807424)

waiting-time distribution

Chen, Anyue and Renshaw, Eric (2004) Markovian bulk-arriving queues with state-dependent control at idle time. Advances in Applied Probability, 36 (2). pp. 499-524. ISSN 1475-6064 (Print), 0001-8678 (Online) (doi:10.1239/aap/1086957583)